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Updated on: 20 Apr 2022, 01:42
Originally posted by abhijay1234 on 19 Apr 2022, 19:46.
Last edited by Bunuel on 20 Apr 2022, 01:42, edited 1 time in total.
Last edited by Bunuel on 20 Apr 2022, 01:42, edited 1 time in total.
Renamed the topic and edited the question.
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C
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Difficulty:
55%
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Question Stats:
60% (01:30) correct
40%
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wrong
based on 443
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The probability that the number of guests at a theme park will exceed 10,000 on Saturday is 0.6. The probability that the number of guests at the same theme park will exceed 10,000 on Sunday is 0.3. Assuming that the numbers of guests on each day are independent, what is the probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both?
A. 0.18
B. 0.46
C. 0.54
D. 0.72
E. 0.9
A. 0.18
B. 0.46
C. 0.54
D. 0.72
E. 0.9
Hello, I was wondering help me understand you go about solving this question. Apparently, the solution subtracts P(Sat and Sun) twice. Would you know why? Thanks
20 Apr 2022, 01:18
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Given: The probability that the number of guests at a theme park will exceed 10,000 on Saturday is 0.6. The probability that the number of guests at the same theme park will exceed 10,000 on Sunday is 0.3.
Asked: Assuming that the numbers of guests on each day are independent, what is the probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both?
The probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both = 0.6*(1-.3) + (1-.6)*.3 = .42 + 12 = .54
IMO C
Asked: Assuming that the numbers of guests on each day are independent, what is the probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both?
The probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both = 0.6*(1-.3) + (1-.6)*.3 = .42 + 12 = .54
IMO C
20 Apr 2022, 06:34
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abhijay1234
if A and B event are independent
P(A intersection B) = P(A) . P(B)
Let A be event that number of guests at the same theme park will exceed 10,000 on Saturday
P(A) = 0.6 ....Given
P(A') = 1-0.6 = 0.4
Let B be event that number of guests at the same theme park will exceed 10,000 on Sunday
P(B) = 0.3 ....Given
P(B') = 1-0.3 = 0.7
the probability that the number of guests exceeds 10,000 on Saturday, or on Sunday, but not both
= P(A).P(B') + P(B).P(A')
= 0.54
