Answer:
a) The probability of being dealt a blackjack hand
[tex]= \frac{64}{1326}[/tex]
b) Approximate percentage of hands winning blackjack hands
[tex]4.827%[/tex]
Step-by-step explanation:
It is given that -
Winning Black Jack means - getting 1 of the 4 aces and 1 of 16 other cards worth 10 points
Thus, in order to win a "black jack" , one is required to pull 1 ace and 1 of 16 other cards
Number of ways in which an ace card can be drawn from a set of 4 ace card is [tex]C^4_1[/tex]
Number of ways in which one card can be drawn from a set of other 16 card is [tex]C^16_1[/tex]
Number of ways in which two cards are drawn from a set of 52 cards is [tex]C^52_2[/tex]
probability of being dealt a blackjack hand
[tex]= \frac{C^4_1* C^16_1}{C^52_2} \\= \frac{4*16}{\frac{51*52}{2} }\\ = \frac{64}{1326} \\[/tex]
Approximate percentage of hands winning blackjack hands
[tex]= \frac{64}{1326} * 100\\= 4.827[/tex]%
