Question

Three cards are dealt from a standard deck of 52. What is the probability of getting:

(a) 2 fives and 1 two? 0.001

(b) at most 2 diamonds? 0.987

(c) not getting a black card?

Please answer all question aight the right answer and explain.

Answer 1

(a) Probability of an event = Favorable number of cases / Total number of cases

Total number of cards = 52

Number of cards drawn = 3

Total number of ways 3 cards are drawn from 52 cards = ( this is total number of cases)

There are 4 five cards and 4 two cards

Number of ways 2 fives and 1 two cards are drawn = ( this is favorable number of cases  )

Probability of getting 2 fives and 1 two cards = 24 / 22100 = 0.001

(b) Number of diamond cards =13

Number of non diamond cards = 52-13 = 39

We have to find the probability of getting at most two diamonds

= Probability of getting 0 diamond or 1 diamond or 2 diamond

Let us find ,

Number of ways of getting 0 diamond

= Number of ways of 0 diamond and 3 non diamond cards

Number of ways of getting 1 diamond

= Number of ways of 1 diamond and 2 non diamond cards

Number of ways of getting 2 diamond

= Number of ways of 2 diamond and 1 non diamond cards

Number of ways at most two diamond cards are drawn = 9139+9633+3042 = 21814

Total number of ways of getting 3 cards = 22100

Probability that at most two diamond cards are drawn = 21814/22100 =0.987

(c) Number of black cards = 26 ( club and spade)

Number of non black cards = 26

Total number of ways 3 cards are drawn = 22100

Number of ways 3 non black cards = 2600

Probability of not getting a black card = = 0.118