Math, asked by candiesandnihilism, 4 months ago

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

Answered by amitnrw
3

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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