Question

You are 1/2 confident that your friend Sally is coming to a party. Given that Sally is at the party, you are 3/4 confident that she will bring her friend Alice to the party. However, Alice never goes to parties without Sally, so given that Sally is not at the party, you are fully confident Alice is not at the party. At the party, you have yet to see Sally, but someone tells you that they know Alice is not at the party. What is the probability that Sally is at the party?

Give you answer in the form: #/#

Answer 1

The probability that Sally is at the party but Alice is not at the party = (the probability that Sally is at the party)*(the probability that Sally bring Alice to the party)

i.e., The probability that Sally is at the party but Alice is not at the party = (1/2)*[1-(3/4)]

i.e., The probability that Sally is at the party but Alice is not at the party = (1/2)*(1/4)

i.e., The probability that Sally is at the party but Alice is not at the party = 1/(2*4)

i.e., The probability that Sally is at the party but Alice is not at the party = 1/8.