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

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A mountain resort will hold its annual one-day snowboarding competitio  [#permalink]

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New post 16 Sep 2018, 23:21
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A
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E

Difficulty:

  45% (medium)

Question Stats:

57% (01:34) correct 43% (01:21) wrong based on 60 sessions

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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%

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Re: A mountain resort will hold its annual one-day snowboarding competitio  [#permalink]

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New post 16 Sep 2018, 23:32
Bunuel wrote:
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%


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
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Re: A mountain resort will hold its annual one-day snowboarding competitio  [#permalink]

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New post 17 Sep 2018, 13:32
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.
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Re: A mountain resort will hold its annual one-day snowboarding competitio  [#permalink]

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New post 18 Sep 2018, 18:47
1
Bunuel wrote:
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%


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
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Re: A mountain resort will hold its annual one-day snowboarding competitio &nbs [#permalink] 18 Sep 2018, 18:47
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