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If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?
- a)1/32
- b)2/25
- c)5/16
- d)8/25
- e)3/4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the probability of rain on any given day in Chicago during the summ...
he period from July 4 to July 8, inclusive, contains 8 – 4 + 1 = 5 days, so we can rephrase the question as “What is the probability of having exactly 3 rainy days out of 5?” Since there are 2 possible outcomes for each day (R = rain or S = shine) and 5 days total, there are 2 x 2 x 2 x 2 x 2 = 32 possible scenarios for the 5 day period (RRRSS, RSRSS, SSRRR, etc…) To find the probability of having exactly three rainy days out of five, we must find the total number of scenarios containing exactly 3 R’s and 2 S’s, that is the number of possible RRRSS anagrams: = 5! / 2!3! = (5 x 4)/2 x 1 = 10 The probability then of having exactly 3 rainy days out of five is 10/32 or 5/16. Note that we were able to calculate the probability this way because the probability that any given scenario would occur was the same. This stemmed from the fact that the probability of rain = shine = 50%. Another way to solve this question would be to find the probability that one of the favorable scenarios would occur and to multiply that by the number of favorable scenarios. In this case, the probability that RRRSS (1st three days rain, last two shine) would occur is (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32. There are 10 such scenarios (different anagrams of RRRSS) so the overall probability of exactly 3 rainy days out of 5 is again 10/32. This latter method works even when the likelihood of rain does not equal the likelihood of shine.
Most Upvoted Answer
If the probability of rain on any given day in Chicago during the summ...
Probability of Rainy Day
Given that the probability of rain on any given day in Chicago during the summer is 50%, we can say that the probability of having a rainy day is 0.5.
Probability of 3 Rainy Days from July 4 to July 8
To find the probability of having exactly 3 rainy days from July 4 through July 8, we can use the binomial probability formula. The formula for binomial probability is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- n is the total number of days (5 days from July 4 to July 8)
- k is the number of successful outcomes (3 rainy days)
- p is the probability of success on any given day (0.5)
Plugging in the values:
P(X = 3) = (5 choose 3) * 0.5^3 * 0.5^(5-3)
P(X = 3) = (10) * 0.125 * 0.125
P(X = 3) = 0.125
Final Answer
Therefore, the probability of having exactly 3 rainy days from July 4 through July 8 is 0.125, which is equivalent to 5/16. Hence, the correct answer is option 'C' - 5/16.
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If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer?
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If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer?.
If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the probability of rain on any given day in Chicago during the summer i s 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?a)1/32b)2/25c)5/16d)8/25e)3/4Correct answer is option 'C'. Can you explain this answer?.
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