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Difficulty:
45%
(medium)
Question Stats:
71% (02:36) correct
29%
(02:05)
wrong
based on 103
sessions
History
Date
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A certain city has a 2/3 chance of rain on Monday, 1/2 chance of rain on Tuesday and 1/3 chance of rain on Wednesday. In the given three-day period, what is the probability that the city experiences rain on at-least 2 days?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/5
_________________
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/5
_________________
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Posts: 43
The probability of rain on Monday is P(M) = 2/3, so probability of no rain on Monday is P(M') = 1/3
Probability of rain on Tuesday is P(T) = 1/2, so probability of no rain on Tuesday is P(T') = 1/2
Probability of rain on Wednesday is P(W) = 1/3, so probability of no rain on Wednesday is P(W') = 2/3
We need to find the probability that the city experiences rain on at-least 2 days.
So P(rain on at-least 2 days) = 1 - {P(rain on no day) + P(rain on 1 day)} =
= 1- {(1/3*1/2*2*3) + (2/3*1/2*2/3) + (1/3*1/2*2/3*) + (1/3*1/2*1/3)}
= 1 -{2/18 + 4/18 + 2/18 + 1/18}
= 1 - 9/18
= 1/2
Hence option C is the right answer.
Probability of rain on Tuesday is P(T) = 1/2, so probability of no rain on Tuesday is P(T') = 1/2
Probability of rain on Wednesday is P(W) = 1/3, so probability of no rain on Wednesday is P(W') = 2/3
We need to find the probability that the city experiences rain on at-least 2 days.
So P(rain on at-least 2 days) = 1 - {P(rain on no day) + P(rain on 1 day)} =
= 1- {(1/3*1/2*2*3) + (2/3*1/2*2/3) + (1/3*1/2*2/3*) + (1/3*1/2*1/3)}
= 1 -{2/18 + 4/18 + 2/18 + 1/18}
= 1 - 9/18
= 1/2
Hence option C is the right answer.
Very simple
Given that prob. of rain on Monday, P(M)=2/3 , lets denote probability of no rain as NP, then NP(M)= 1-2/3= 1/3
Prob. of rain on Tuesday, P(T)= 1/2 similarly, NP(T)= 1-1/2= 1/2
Prob. of rain Wednesday, P(W)=1/3 and NP(W)= 1-1/3= 2/3
We have to find Prob. of rain on at least 2 days out of 3.
It will have two components probability of rain on exactly 2 days out of 3 and Prob of rain on all 3 days.
Calculation: REQUIRED PROBABLITY = P(M)*P(T)*NP(W)+P(M)*NP(T)*P(W)+NP(M)*P(T)*P(W)+ P(M)*P(T)*P(W)
= 2/3*1/2*2/3+ 1/3*1/2*1/3+ 2/3*1/2*1/3+ 2/3*1/2*1/3 = 1/2
Given that prob. of rain on Monday, P(M)=2/3 , lets denote probability of no rain as NP, then NP(M)= 1-2/3= 1/3
Prob. of rain on Tuesday, P(T)= 1/2 similarly, NP(T)= 1-1/2= 1/2
Prob. of rain Wednesday, P(W)=1/3 and NP(W)= 1-1/3= 2/3
We have to find Prob. of rain on at least 2 days out of 3.
It will have two components probability of rain on exactly 2 days out of 3 and Prob of rain on all 3 days.
Calculation: REQUIRED PROBABLITY = P(M)*P(T)*NP(W)+P(M)*NP(T)*P(W)+NP(M)*P(T)*P(W)+ P(M)*P(T)*P(W)
= 2/3*1/2*2/3+ 1/3*1/2*1/3+ 2/3*1/2*1/3+ 2/3*1/2*1/3 = 1/2
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