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03 Jan 2019, 11:49
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:13) correct
27%
(01:21)
wrong
based on 211
sessions
History
Date
Time
Result
Not Attempted Yet
The probability of rain is 1/2 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?
(A) 1/2
(B) 31/32
(C) 63/64
(D) 127/128
(E) 5/2
(A) 1/2
(B) 31/32
(C) 63/64
(D) 127/128
(E) 5/2
UB001
Joined: 26 Dec 2018
Last visit: 10 Apr 2022
Posts: 106
Given Kudos: 91
Location: India
Schools: Mannheim"20 Smurfit "20 NUS '21 NTU '20
03 Jan 2019, 11:55
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The probability of rain is 1/2 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?
Probability of an Event Happening + Probability of that Event Not Happening = 1
Probability of Rain = 1 /2
Probability of No Rain =1- 1/2 = 1/2
For the five day period the Probability of No Rain = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
For the Five day period the Probability of Rain = 1- 1/32 = 31/32
Answer Option B is Correct
Probability of an Event Happening + Probability of that Event Not Happening = 1
Probability of Rain = 1 /2
Probability of No Rain =1- 1/2 = 1/2
For the five day period the Probability of No Rain = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
For the Five day period the Probability of Rain = 1- 1/32 = 31/32
Answer Option B is Correct
04 Jan 2019, 03:05
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Solution
Given:
- • The probability that it rains is \(\frac{1}{2}\) for every day in the next week
To find:
- • The probability that it rains on at least one working day
Approach and Working:
P(E) = 1 – P(non-event)
- • In this case, P(non-event) = the probability that it does not rain on any working day = \(\frac{1}{2}* \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{2^5} = \frac{1}{32}\)
Therefore, P(E) = \(1 – \frac{1}{32} = \frac{31}{32}\)
Hence, the correct answer is Option B
Answer: B
