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.)
Accepted Solution
A:
Answer: 0.05699Step-by-step explanation:The total number of cards in a deck = 52The total number of black cards = 26Then ,[tex]\text{P(Black)}=\dfrac{C(26,4)}{C(52,4)}=0.00182842367\approx0.00183[/tex]The total number of face cards = 12Then , [tex]\text{P(Face)}=\dfrac{C(12,4)}{C(52,4)}\approx0.05522[/tex]The number of cards that are black and face cards = 6Then , [tex]\text{P(Black and Face )}=\dfrac{C(6,4)}{C(52,4)}\approx0.00006[/tex]Then , the probability that a randomly drawn hand of four cards contains all black cards or all face cards is given by :-[tex]\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[/tex]