Problem Solving

BTGmoderatorDC wrote: ↑

Sun Dec 25, 2022 5:49 pm

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%


OA E

Source: Veritas Prep

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

BTGmoderatorDC wrote: ↑

Sun Dec 25, 2022 5:49 pm

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%


OA E

Source: Veritas Prep

We see 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