Question

You are playing blackjack and want to know the probability of getting dealt certain cards. In blackjack two cards are drawn from a deck, the first is dealt to you face down and the second is dealt face up. Using the product rule, find the probability that (a) The bottom card is an ace or a king and the top card is red. (b) Both of the cards are clubs. (c) At least one of the cards is a jack.

Answer 1

The correct answer is:

(a) 0.0784

(b) 0.0588

(c) 0.1493

Explanation:

According to the question,

Number or ace or king,

n (ace or king) = 8

Number of red,

n (red) = 26

Number of club,

n (club) = 13

Number or jack,

n (jack) = 4

(a)

Probability of 1st ace or king and 2nd in red will be:

⇒
`P(ist \ ace \ or \ king \ and \ 2nd \ red) = (8)/(52)*(26)/(51)`

⇒
`=0.0784`

(b)

Probability of both clubs will be:

⇒
`P(clubs) =(13C_2)/(52C_2)`

⇒
`=0.0588`

(c)

Probability of at least one is jack will be:

⇒
`P(at \ least \ one \ is \ jack)=1-P(none \ jack)`

⇒
`=1-(48C_2)/(52C_2)`

⇒
`=0.1493`