Anny, Betty, Cindy and Dolly were all friends at school. Subsequently each of the 6 pairs...

Anny, Betty, Cindy and Dolly were all friends at school. Subsequently each of the 6 pairs meet up; at each of the 6 meetings the pair involved quarrel with some fixed probability p, or become firm friends with probability q=1-p. Quarrels take place independently of each other. In future, if any of the 4 hears a rumour, then she tells it to her firm friends only. If Anny hears a rumour, what is the probability that

(a) Dolly hears it if Anny and Betty have quarrelled?

(b) Dolly hears it if Betty and Cindy have quarrelled?

Express your answer in terms of q.

Solutions

Expert Solution

a)Anny and Betty have quarrelled with probability

The probability that the rumour Anny heard will pass to Dolly if Anny and Betty have quarrelled is

Case 1) Anny to Dolly. Anny and Dolly are friends with probability .

Case 2) Anny to Cindy then Cindy to Dolly. Anny and Cindy and Cindy and Dolly are frieds with probability .

So the required probability is .

b)Cindy and Betty have quarrelled with probability

The probability that the rumour Anny heard will pass to Dolly if Cindy and Betty have quarrelled is

Case 1) Anny to Dolly. Anny and Dolly are friends with probability .

Case 2) Anny to Cindy then Cindy to Dolly. Anny and Cindy and Cindy and Dolly are frieds with probability .

Case 3) Anny to Betty then Betty to Dolly. Anny and Betty and Betty and Dolly are frieds with probability .

So the required probability is .

orchestra answered 1 year ago

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