Question

Two cards are drawn with replacement in succession. What is the probability that both cards drawn are Queen?1/16916/171/23/51

Answer 1

Given:

Two cards are drawn with replacementss in succession.

Required:

We need to find the probability that both cards are drawn is Queen.

Step-by-step explanation:

The sample space = The number of cards.

`n(S)=52`

Let A be the event of drawing a queen.

The favourable outcomes =The number of queen cards.

`n(A)=4`

The probability of drawing the first card, which is queen.

`P(A)=(n(A))/(n(S))=(4)/(52)=(1)/(13)`

The card is replaced.

Let B be the event of drawing the second card after replacement.

The probability of drawing the second card, which is queen is equal to the probability of drawing the first card, which is queen.

`P(B)=P(A)=(1)/(13)`

The probability that both cards drawn are Queen.

`P(both\text{ cards are queen\rparen=P\lparen A\rparen}* P(B)=(1)/(13)*(1)/(13)`
`P(both\text{ cards are queen\rparen}=(1)/(169)`

Final answer:

`P(both\text{ cards are queen\rparen}=(1)/(169)`