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The probability of the occurrence of event A is 0.50

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The probability of the occurrence of event A is 0.50  [#permalink]

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New post 07 Oct 2018, 02:18
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The probability of the occurrence of event A is 0.50. The probability of the occurrence of event B is 0.40. What is the range of probability A will not happen AND B will not happen?

A. 0.1≤p≤0.5
B. 0.4≤p≤0.5
C. 0.5≤p≤0.6
D. 0.1≤p≤0.6
E. 0.2≤p≤0.5
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Re: The probability of the occurrence of event A is 0.50  [#permalink]

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New post 07 Oct 2018, 05:55
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trankimphuong wrote:
The probability of the occurrence of event A is 0.50. The probability of the occurrence of event B is 0.40. What is the range of probability A will not happen AND B will not happen?

A. 0.1≤p≤0.5
B. 0.4≤p≤0.5
C. 0.5≤p≤0.6
D. 0.1≤p≤0.6
E. 0.2≤p≤0.5


Prob ( no(A) and no(B))
least
Let the events be mutually exclusive, Example :- toss of a coin, and probability of head and probability of tails
so there is NO overlap and P(noA and noB)=1-(0.5+0.4)=1-0.9=0.1
[b]Max
Let the events be independent that both can occur at the same time :- prob of head as event A and probability of 3 or 6 in throw of a dice as B
So there can be complete overlap too so probability = 1-(0.5)=0.5

Answer - 0.1≤p≤0.5

A
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Re: The probability of the occurrence of event A is 0.50  [#permalink]

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New post 07 Oct 2018, 21:58
Could you please provide a more detailed explanation for the answer? I'm weak in Probability.
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Re: The probability of the occurrence of event A is 0.50  [#permalink]

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New post 07 Oct 2018, 22:27
chetan2u wrote:
trankimphuong wrote:
The probability of the occurrence of event A is 0.50. The probability of the occurrence of event B is 0.40. What is the range of probability A will not happen AND B will not happen?

A. 0.1≤p≤0.5
B. 0.4≤p≤0.5
C. 0.5≤p≤0.6
D. 0.1≤p≤0.6
E. 0.2≤p≤0.5


Prob ( no(A) and no(B))
least
Let the events be mutually exclusive, Example :- toss of a coin, and probability of head and probability of tails
so there is NO overlap and P(noA and noB)=1-(0.5+0.4)=1-0.9=0.1
[b]Max
Let the events be independent that both can occur at the same time :- prob of head as event A and probability of 3 or 6 in throw of a dice as B
So there can be complete overlap too so probability = 1-(0.5)=0.5

Answer - 0.1≤p≤0.5

A



for the independent events, should the probability be 1- (A + B - overlap) = 1 - (0.5 + 0.4 - 0.2) = 0.3
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The probability of the occurrence of event A is 0.50  [#permalink]

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New post 15 Oct 2018, 10:46
P(not A and Not B) = [1-p(A)][1-p(B)]
= 1+ P(A)*P(B) -P(A) - P(B)

For this expression to be maximum, P(A)*P(B) should be maximized
Since we dont know the relation between A and B. The max A*B can be is 0.4
So We have 1+0.4 -0.5 - 0.4 = 0.5

For this expression to be minnimized A*B should be zero , this can happen when A and B are mutually exclusive events
----
1+0 -0.5 -0.4 = 0.10

A


.....
chetan2u My first break up of equation P(not A and Not B) = [1-p(A)][1-p(B)] , is that correct. Even if we dont know the relation of A and B.
Did you also come up with the equations like I did ?
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Re: The probability of the occurrence of event A is 0.50  [#permalink]

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New post 16 Oct 2018, 18:17
1
trankimphuong wrote:
The probability of the occurrence of event A is 0.50. The probability of the occurrence of event B is 0.40. What is the range of probability A will not happen AND B will not happen?

A. 0.1≤p≤0.5
B. 0.4≤p≤0.5
C. 0.5≤p≤0.6
D. 0.1≤p≤0.6
E. 0.2≤p≤0.5


If events A and B are mutually exclusive (i.e., sets A and B are disjoint), then the probability the two events will not happen is 1 - 0.5 - 0.4 = 0.1. If set B is a subset of set A (i.e., set B is inside of set A), then the probability the two events will not happen is 1 - 0.5 = 0.5. Therefore, the probability ranges from 0.1 to 0.5.

Answer: A.
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Re: The probability of the occurrence of event A is 0.50 &nbs [#permalink] 16 Oct 2018, 18:17
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