need help on Conditional Probability problems...

[Dipti Ranjan Biswal]

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.

Thanks in Advance,
DRB

[BGM]

p0 = p1 = a, Pk = (1-2a)2^–(a-1) (k >= 2)

It should be such that the sum is equal to 1.

Question 2 you need to provide the table as well.

But anyway both question are very elementary and standard, no tricky thing at all. Directly apply the definition of conditional probability is ok.
So show us your effort when you have any further question and come back.