Question

Wo cards are drawn without replacement from standard deck of 52 cards. What is the probability that the first card is a club and the second card is a diamond and are these events independent?

1 / 2 ; Yes, they are independent events


13 / 204 ; No, they are dependent events


1 / 17 ; No, they are dependent events


103 / 204 ; Yes, they are independent events

Answer 1

"13 / 204 ; No, they are dependent events "

Explanation:

The probability of getting a club at first throw is simply total number of clubs divided by total number of cards in the deck.

Total clubs is 13

Total cards in deck is 52

Hence, P(clubs) =
`(13)/(52)`

Since the first card IS NOT replaced, the deck has now 51 cards. We want probability of diamond. There are still 13 diamonds, so probability of diamond now would be 13/51

Hence, Probability that first card is a club and the second card is a diamond should be 13/52 MULTIPLIED by 13/51

P(1st Club, 2nd Diamond) =
`(13)/(52)*(13)/(51)=(13)/(204)`

Note: They are dependent events since we are calculating probability without replacement. The first draw affected the total number of cards in the 2nd draw.

2nd answer choice is right.