Question

Katy chose a card at random from a deck of 52 cards. Katy replaced the first card and then chose a second card. What is the probability that Katy chose a diamond both times?

Answer 1

There are 13 cards in the suit of diamonds. The probability of randomly choosing a diamond is 13/52 = 1/4. The two events 'draw a diamond' are independent, therefore the probability of drawing a diamond both times is:

`P(diamond\ both\ times)=(1)/(4)*(1)/(4)=?`

Answer 2

Answer: Our required probability is
`(1)/(16)`

Explanation:

Since we have given that

Number of cards in deck = 52

Number of diamond in a deck = 13

So, Probability of getting diamond in first time =
`(13)/(52)=(1)/(4)`

she replaced the first card, then chose a second card.

So, probability of getting diamond second time =
`(13)/(52)=(1)/(4)`

So, Probability that she chose a diamond both times is given by

`(1)/(4)* (1)/(4)\\\\=(1)/(16)`

Hence, our required probability is
`(1)/(16)`