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D
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91% (02:00) correct
9%
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On the planned day of a picnic, there is a 40% probability of rain. If it rains, there is a 90% probability that the picnic will be canceled, but if it doesn't rain, there is a 95% probability that the picnic will take place. What is the probability that the picnic will take place?
A. 47%
B. 49%
C. 53%
D. 61%
E. 73%
A. 47%
B. 49%
C. 53%
D. 61%
E. 73%
11 Feb 2025, 01:50
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| Rain | No Rain | Total | |
| Probability of rain | 0.4 | 0.6 | |
| Probability of picnic | 0.1 | 0.95 | |
| Combined | 0.04 | 0.57 | 0.61 |
Probability that the picnic will take place = 61%
Bunuel
11 Feb 2025, 03:26
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P(Rain) = .4
P(No Rain) = .6
P(No Picnic| Rain) = .4*.9
Hence P(Picnic| Rain) = .4*.1
Also P(Picnic| No rain) = .6 * .95
Hence P(rain) = P(Picnic| Rain) + P(Picnic| No rain)
= (.4*.1) + (.6 *.95)
= .61
IMO Ans D
P(No Rain) = .6
P(No Picnic| Rain) = .4*.9
Hence P(Picnic| Rain) = .4*.1
Also P(Picnic| No rain) = .6 * .95
Hence P(rain) = P(Picnic| Rain) + P(Picnic| No rain)
= (.4*.1) + (.6 *.95)
= .61
IMO Ans D
