A mountain resort will hold its annual one-day snowboarding

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

A mountain resort will hold its annual one-day snowboarding

by BTGmoderatorDC » Tue Feb 12, 2019 7:13 pm

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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%

OA E

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Feb 12, 2019 7:13 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 13, 2019 6:18 am

BTGmoderatorDC 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%

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Feb 15, 2019 5:14 pm

BTGmoderatorDC 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%

OA E

Source: Veritas Prep

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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