If the probability of rain on any given day is 50%, what is

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by AAPL » Sat Feb 02, 2019 7:32 am

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Veritas Prep

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?

A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2

OA B

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Source: Beat The GMAT — Problem Solving | Sat Feb 02, 2019 7:32 am

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by [email protected] » Sat Feb 02, 2019 11:27 am

Hi All,

We're told that the probability of rain on any given day is 50%. We're asked for the probability that it will rain on AT LEAST three days in a ROW during a five-day period. This question can be approached in a number of different ways; you might find it easiest to do a little math and 'map out' the various possible ways to get at least 3 days of rain in a row.

Since there are two events (rain or no rain) that have an equal chance of occurring each day, with 5 days in a row, there are (2)(2)(2)(2)(2) = 32 possible outcomes for the 5 days. The number of outcomes that include AT LEAST 3 days of rain IN A ROW are....

3 days:
RRRNN
NRRRN
NNRRR

4 days:
RRRRN
RRRNR
RRNRR
RNRRR
NRRRR

5 days:
RRRRR

8 options out of 32 total = 8/32 = 1/4

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Feb 06, 2019 6:24 pm

AAPL wrote:Veritas Prep

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?

A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2

OA B

Let R = rain and N = no rain. To have rain on at least three days in a row during a five-day period, we could have:

RRRNN, NRRRN, NNRRR, RRRRN, NRRRR, RNRRR, RRRNR, or RRRRR.

Notice that the probability of R is Â½ and the probability of N is also Â½. Thus, the probability of any of the scenarios above is Â½ x Â½ x Â½ x Â½ x Â½ = (Â½)^5 = 1/32. Since we have a total of 8 scenarios, the overall probability is 8 x 1/32 = 1/4.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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