Can anybody please help me to work out on following problems?
1. The probability Pk that a family has ‘k’ children is given by p0 = p1 = a, Pk = (1-2a)2^–(a-1) (k >= 2). It is known that a family has two boys. What is the probability that: (a) the family has only two children? (b) the family has two girls as well?
(^ - to the power)
2. An amplifier may burn one or both of its fuses if one or both of outs tubes are defective. Let the events: A1: only tube I is defective (i=1,2); A3: both tubes are defective; Bj: fuse j burns out (j=1,2) ; B3: both fuses burn out. The conditional probabilities of burning the fuses appear in the following table: Find the probabilities that (a) both tubes are defective given that both fuses were burnt out; (b) only tube 2 is defective given that both fuses were burnt out. (c) only tube 2 is defective given that at least one fuse burnt out. The events A1, A2, A3 have probabilities 0.3, 0.2, 0.1 respectively.