A mountain resort will hold its annual one-day snowboarding competitio

Question

A mountain resort will hold its annual one-day snowboarding competition if it snows on either Saturday or Sunday, but if it does not snow at all it will not hold the event. If there is a 70% chance that it snows on any given day at the resort, what is the probability that the event will be held?

A. 70%
B. 80%
C. 81%
D. 90%
E. 91%

A. 70%
B. 80%
C. 81%
D. 90%
E. 91%

ScottTargetTestPrep · Accepted Answer

We see that that they will NOT hold the event only if it does not snow on Saturday and it does not snow on Sunday. Since the probability is 0.7 that it will snow on any given day, we see that the probability that it will NOT snow on any given day is (1 - 0.7) = 0.3. We can use the formula:

P(hold the event) = 1 - P(not hold the event)

P(not hold the event) = 0.3 x 0.3 = 0.09.

So P(hold the event) = 1 - 0.09 = 0.91 = 91%

Answer: E

honneeey · Answer

Chances of Snow on a given day is =0.7

So there are 3 possibilities for competition to take place= Snows on Saturday and on Sunday+Snows on Saturday but not on Sunday+NO snow on Saturday but snows on Sunday

Snow on any day=Snow on Sunday=Snow on Sunday=0.7
No snow on any day=No Snow on Sunday=No Snow on Sunday=1- 0.7=0.3

as both the events are mutually exclusive

=0.7*0.7 +0.7*0.3+0.3*0.7
=0.49+0.21+0.21
=0.91
=91%

Answer is E

US09 · Answer

Probability that it snows on a day=70%, probability that it does not now=30%.
Probability that it does not snow on both of the days= 0.3 * 0.3 = .09 or 9%

Hence, probability that it snows on either of the days= 1-9/100 = 91%.

Therefore, E.

BrentGMATPrepNow · Answer

GIVEN: P(snow) = 0.7, so P(no snow) = 0.3

Let's use the complement to solve this.
That is,  P(event is held) = 1 -  P(event is NOT held)

P(event is NOT held)  = P(no snow on Saturday   AND   no snow on Sunday)
= P(no snow on Saturday)   x   P(no snow on Sunday)
= 0.3   x   0.3
=  0.09

So,  P(event is held) = 1 -  0.09  
= 0.91

Answer: E

Cheers,
Brent

apati10 · Answer

Can we solve it like this?

P(it rains on Saturday)= 0.7
P(it rains on Sunday)= 0.7

P(match held)=
Rains on Saturday OR doesn't rain on Saturday*rains on Sunday

= 0.7 + 0.3*0.7
= 0.91

= 91%

Posted from my mobile device

HoneyLemon · Answer

In approaching this conditional probability problem it is important to recognize that you do not need it to snow BOTH days in order for the event to run: as long as it rains on one or the other the event will be held. So this problem is asking for the probability of snow on either Saturday or Sunday. There are a few ways to determine this probability.

One is to note that if it snows Saturday (70%), then the event will run, but that if it does NOT snow Saturday (30%) then there's a 70% probability that it will still snow Sunday. So the two sequences of "Snows Saturday" or "Doesn't Snow Saturday, but then Snows Sunday" will combine for the total probability of the event running:

Snows Saturday = 70%
Does Not Snow Saturday, then Snows Sunday = (30%)(70%) = 21%

Snows either Saturday or Sunday = 70% + 21% = 91%. Choice (E) is correct.

You could also note that the only outcome that does NOT work for you is if it fails to snow both days. Everything else does work, so you could subtract the probability of "No Snow, then No Snow" from 100% to get to the total:

100% - Neither
100% - (30%)(30%) = 100% - 9% = 91%, so choice (E) is correct.

Of course, you could also use the "General Case" probability formula: Probability A + Probability B - Probability Both = Probability of A or B

Here that's 70% + 70% - (70%)(70%) = 140% - 49% = 91%. Again, choice (E) is correct.

Basshead · Answer

P(Snow) = 0.7
P(No Snow) = 0.3

If it snows on Saturday = 0.7
If it does not snow on Saturday and snows on Sunday = 0.7 * 0.3 = 0.21

0.7 + 0.21 = 0.91

Krishnahelps · Answer

ScottTargetTestPrep   Bunuel   KarishmaB  , In such cases why don't we consider snowing on both the days? Also, usually for either or do we need to not consider snowing on both days?

KarishmaB · Answer

We are considering snow on both the days. If it snows on both the days, the competition will take place. Look, there are 4 possibilities: Snow on Saturday, no snow on Sunday. Probability = 0.7 * 0.3 No snow on Saturday, snow on Sunday. Probability = 0.3 * 0.7 Snow on Saturday, snow on Sunday. Probability = 0.7 * 0.7 No snow on Sat, no snow on Sun. Probability = 0.3 * 0.3 When will the competition take place? In the first three cases: 0.7 * 0.3 + 0.3 * 0.7 + 0.7 * 0.7 = 0.91 or we can say that it will not take place with probability 0.09 and hence it will take place will probability 1 - 0.09 = 0.91 Answer (E) Check this video on Probability: https://youtu.be/0BCqnD2r-kY

bumpbot · Answer

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