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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The probability that event M will not occur is 0.8 and the probability

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Intern  B
Joined: 12 Sep 2018
Posts: 3
Location: United States
Schools: HBS '22 (S)
GMAT 1: 750 Q49 V44
GPA: 3.6
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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mskx wrote:
How to you calculate P(M and R) that you get 0?

and means multiply

P(M or R) = P(M) + P(R) - P(M and R)
P(M or R) = P(0.9) + P(0.9) - P(0.9*0.9) -> 0.9*0.9 is not 0
But please consider that P(M or R) = P(M) + P(R) -P(M and R) is wrong because its a mutually exclusive event.

Because they're mutually exclusive, P(M and R) can't happen. That's why I used 0. So really it's P(M or R)=P(M) + P(R). If P(M) and P(R) are each 0.9 (mutually exclusive of course), the P(M or R) becomes 1.8, which is what doesn't make sense to me.
Manager  S
Joined: 24 Dec 2017
Posts: 183
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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M will not occur = 0.8
M will occur = 0.2

R will not occur = 0.6
R will occur = 0.4

Probability that either event M or event R will occur = 0.2 + 0.4 = 0.6 (3/5)

Hence C
Manager  G
Joined: 23 Jan 2018
Posts: 220
Location: India
WE: Information Technology (Computer Software)
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Dear experts,
P(M)=.8, Hence P(M')=.2
P(R)=.6, So P(R')=.4
P(Either of the events)=P(M' and R) OR P(R' and M)=(.2*.6)+(.8*.4)=.44.

Can some one please explain what I am missing here.

Regards,
Arup
Director  G
Joined: 09 Mar 2018
Posts: 990
Location: India
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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2
Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

I will use the 2*2 matrix here

MO= M will occur
MNO= M will not occur

All the values are given, and we need to find

--------MO--------MNO
-RO----0----------0.4-----0.4
RNO---0.2--------0.4-----0.6
-------0.2---------0.8------1

either event M or event R will occur, this will be again => 1 - (both will occur), Since in probability P(happening) + P(not happening) = 1
1-0.4 =0.6

C
_________________
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Intern  B
Joined: 23 Aug 2016
Posts: 13
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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shonakshi wrote:
Can someone please explain why is it not
0.8*0.4+0.2*0.6
11/25 This is not right as you are confusing between Event and Occurrence of the event. Your formula would be true if you try to find out, probability of EXACTLY one of M or R will occur, when the other WILL NOT occur. This is NOT same as 'probability of M or R to occur'.
I will illustrate with an example. Scenario 1: You are tossing a coin 2 times. What's the probability of getting EXACTLY one head? Your above formula will work in this case. There are 2 occurrences of toss here. Also, P(H) = 1/2 and P(T) = 1/2. Get EXACTLY one head in two tosses = P(H).P(~T) + P(~H).P(T) = 1/2. [without formula: HT (valid), TH (valid), HH (invalid), TT (invalid). Hence : 2/4 = 1/2]
Scenario 2: What is the probability of getting a head OR tail when you toss a coin? Note: here it is talking about only one occurrence of toss. Here the formula should be P(H or T) = P(H) + P(T) - P(H and T). P(H and T) is obviously 0. So, P(H or T) = 1/2 + 1/2 = 1 (it's a certainty). [now without formula: it is a guarantee in a coin toss that you will either get head or tail. so, probability = 1 ]

This question in OP is the second scenario described above, hence your formula won't give you correct result. Hope it helps !!
Manager  B
Joined: 25 Sep 2018
Posts: 66
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

M will occur =1-.8=.2
R will occur =1-.6=.4

P(M or R)=P(M)+P(R)-P(M & R)
=.2+.4-0
=.6=3/5

Posted from my mobile device
Intern  B
Joined: 31 Oct 2018
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Location: Switzerland
Schools: Tsinghua
GPA: 3.25
WE: Sales (Consumer Products)
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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After months of just reading this forum's precious advice, I'll give it a go and ask a question for the first time.

Just went through all the OG questions, and this one was the earliest that messed with my mind:

My Idea is that the Probability that neither A nor B occurs is 0.6 x 0.8 = 0.48 the rest 0.52 (minus the Probability that both occur, = 0) is the result.

Can someone explain why that approach is wrong.

Thanks
Intern  B
Joined: 23 Nov 2018
Posts: 28
The probability that event M will not occur is 0.8 and the probability  [#permalink]

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A lot of users have tried explaining why
0.8*0.4+0.2*0.6
11/25
is wrong, but I think the confusion still stands

We understand why the correct soln is correct but we don't understand why our soln is incorrect. Can you help us bridge the gap?
Thanks for your time and help Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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2
legendinthewomb wrote:

A lot of users have tried explaining why
0.8*0.4+0.2*0.6
11/25
is wrong, but I think the confusion still stands

We understand why the correct soln is correct but we don't understand why our soln is incorrect. Can you help us bridge the gap?
Thanks for your time and help Hi

It is given that both events A and B will NOT occur together, so when you take one occurring say A =0.4, other B NOT occurring is not 0.8, it is 1 or 100% because it is sure that B will not occur when A is occurring. So answer is 0.2+0.4=0.6
Say you have only 20 cards of a pack of 52 cards. Probability of picking not picking an A is 0.9 and probability of not picking King is 0.8.
Probability of picking any one will be straight sum of individual probabilities that is 0.1+0.2 because they cannot occur together.
_________________
Intern  B
Joined: 23 Nov 2018
Posts: 28
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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chetan2u wrote:
legendinthewomb wrote:

A lot of users have tried explaining why
0.8*0.4+0.2*0.6
11/25
is wrong, but I think the confusion still stands

We understand why the correct soln is correct but we don't understand why our soln is incorrect. Can you help us bridge the gap?
Thanks for your time and help Hi

It is given that both events A and B will NOT occur together, so when you take one occurring say A =0.4, other B NOT occurring is not 0.8, it is 1 or 100% because it is sure that B will not occur when A is occurring. So answer is 0.2+0.4=0.6
Say you have only 20 cards of a pack of 52 cards. Probability of picking not picking an A is 0.9 and probability of not picking King is 0.8.
Probability of picking any one will be straight sum of individual probabilities that is 0.1+0.2 because they cannot occur together.

Got it! Basically we misunderstood the question (or question doesn't have as much clarity as we'd like it to have).

It means: Only one event can be happen regardless of whether it fails or not.
What it doesn't mean: Both these events can't happen simultaneously ie both of them succeeding at the same time. They can occur simultaneously but only one event can be successful.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5723
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

M will not occur- 0.8 and will occur = .2
R will not occur = .6 and will occur = .4
either event M or event R will occur
.2+.4 ; .6 ; 6/10 ; 3/5
IMO C
SVP  D
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34 Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25

The probability that event M will occur is 0.2
The probability that event R will occur is 0.4

The probability that either event M or event R will occur = .2 + .4 = .6 = 3/5 since events M and R cannot both occur

IMO C
SVP  D
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34 The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Bunuel wrote:
The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

A) 1/5
B) 2/5
C) 3/5
D) 4/5
E) 12/25
[/quote]

The probability that event M will occur is 1-.8 = 0.2
The probability that event R will occur is 1- .6 = 0.4

The probability that either event M or event R will occur = .2 + .4 = .6 = 3/5 since events M and R cannot both occur

IMO C
Intern  B
Joined: 18 Jul 2018
Posts: 31
The probability that event M will not occur is 0.8 and the probability  [#permalink]

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My mistake:

I misunderstood "M and R cannot both occur" as calculating for P(M)+P(R)-2*P(M & R), instead of thinking M & R as mutually exclusive events and therefore P(M & R) = 0.
Manager  G
Joined: 13 Nov 2018
Posts: 134
Location: India
GMAT 1: 700 Q51 V32
Re: The probability that event M will not occur is 0.8 and the probability  [#permalink]

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Easy one -testing concept of mutually exclusive events in probability
P(R) = 1 - 0.8= 0.2
P(M) = 1 -0.6 = 0.4

Both events cannot occur simultaneously, so r and m are mutually exclusive

Prob that either event M or event R will occur = 0.2+0.4 = 0.6 = 6/10 = 3/5 Re: The probability that event M will not occur is 0.8 and the probability   [#permalink] 08 Dec 2019, 04:04

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