Question

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards then the mean of the number of aces is

Answer 1

Answer:

no. favourable cases/total number of outcomes.

4/52 is the correct answer✅

Answer 2

Answer:

Total no. of cards = 52

Total no. of aces = 4

P(ace)=

52

4

=

13

1

P(non−ace)=

52

48

=

13

12

Let X be a random variable, such that

X = no. of aces obtained in 2 draws.

Case I:- X = 0 (No aces are obtained)

P(X=0)=P(non-ace and non-ace)

=P(non−ace)×P(non−ace)

=

13

12

×

13

12

=

169

144

Case II:- X = 1 (1 ace is obtained)

P(X=1)=P((ace and non-ace) or (non-ace and ace))

=(P(non−ace)×P(non−ace))+(P(ace)×P(non−ace))

=(

13

12

×

13

1

)+(

13

1

×

13

12

)

=

169

24

Case III:- X = 2 (two aces are obtained)

P(X=2)=P(ace and ace)

=P(ace)×P(ace)

=

13

1

×

13

1

=

169

1