Question

Consider a couple who gave birth to 4 children (assume a boy is equally likely as a girl) The events space for the experiment S={GGGG,GGGB,GGBG,GGBB,GBGG,GBGB.GBBG GBBB,BGGG BGGB,BGBG,BGBB,BBGG,BBGB,BBBG BBBB } Find the probability of the event E1 of no more than 2 girls in the family () Find the probability of event E2 of no less than two boys in the family (i) (ii) Find the probability of E1 n E2 E1 U E2 (iv) Find the probability of Number Number (i1) (ii)Number Number (iv)

Answer 1

1)

Favorable outcomes = {GGBB,GBGB,GBBG,GBBB,BGGB,BGBG,BGBB,BBGG,BBGB,BBBG,BBBB}

Number of favourable outcomes = 11

Total number of outcomes = 16

So,

0.6875 16 P(E)

2)

Favorable outcomes = {GGBB,GBGB,GBBG,GBBB,BGGB,BGBG,BGBB,BBGG,BBGB,BBBG,BBBB}

Number of favourable outcomes = 11

Total number of outcomes = 16

So,

0.6875 P(E2) 16

3)

Favorable outcomes = {GGBB,GBGB,GBBG,GBBB,BGGB,BGBG,BGBB,BBGG,BBGB,BBBG,BBBB}

Number of favourable outcomes = 11

Total number of outcomes = 16

So,

P(E1 n E2) = 0.6875 16

4)

We know that

P(E UE2) P(E)+ P(E2) - P(En E2}

So,

P(EUE 0.68750.6875 0.6875 0.6875