You are considering asking L out for a date but you are a little worried that L may
already have started dating somebody else. The probability that L is dating somebody else is 0.25. If L is dating somebody else s/he is unlikely to accept your offer to go on a date; in fact you think the probability (of accepting your proposal) is 1/6. If L is not dating somebody else, though you think the probability is much better about 2/3.
a) What is the probability that L is dating somebody else and accepts your proposal to
go on a date?
b) What is the probability that L will accept your offer to go on a date?
c) What is the probability that L is dating somebody else, given that L agreed to go on
a date?
Answers
Given : The probability that L is dating somebody else is 0.25. If L is dating somebody else the probability (of accepting your proposal) is 1/6. If L is not dating somebody else, though you think the probability is 2/3
To Find: a) What is the probability that L is dating somebody else and accepts your proposal to go on a date?
b) What is the probability that L will accept your offer to go on a date?
c) What is the probability that L is dating somebody else, given that L agreed to go on a date?
Solution:
The probability that L is dating somebody else is 0.25
The probability that L not dating somebody else is 1- 0.25 = 0.75
Probability of selecting proposal for dating if already dating = 1/6
Probability of not selecting proposal for dating if already dating =1- 1/6 = 5/6
Probability of selecting proposal for dating if already not dating = 2/3
Probability of not selecting proposal for dating if already not dating =1- 2/3 = 1/3
probability that L is dating somebody else and accepts your proposal to go on a date = 0.25 x (1/6)
= 1/24
= 0.04167
probability that L will accept your offer to go on a date
= (0.25)(1/6) + (0.75)(2/3)
= 1/24 + 1/2
= 13/24
= 0.54167
L is dating somebody else, given that L agreed to go on a date
= (1/24)/(13/24)
= 1/13
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