Question

What is the probability that a randomly drawn hand of four cards contains all black cards or all face cards? The probability is 6 Round to four decimal places as needed.)

Answer 1

Answer: 0.05699

Step-by-step explanation:

The total number of cards in a deck = 52

The total number of black cards = 26

Then ,$\text{P(Black)}=\dfrac{C(26,4)}{C(52,4)}=0.00182842367\approx0.00183$

The total number of face cards = 12

Then , $\text{P(Face)}=\dfrac{C(12,4)}{C(52,4)}\approx0.05522$

The number of cards that are black and face cards = 6

Then , $\text{P(Black and Face )}=\dfrac{C(6,4)}{C(52,4)}\approx0.00006$

Then , the probability that a randomly drawn hand of four cards contains all black cards or all face cards is given by :-

$\text{P(Black or Face)}=\text{P(Black)+P(Face)-P(Black and Face)}\\\\\Rightarrow\ \text{P(Black or Face)}=0.00183+0.05522-0.00006\\\\\Rightarrow\ \text{P(Black or Face)}=0.05699$