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Amar keeps picking playing cards out of a standard deck of 52 cards in the hopes that he will
draw a spade. There are 13 spades in the deck. After looking at each card, he places it back in
the deck. What is the probability that Amar will draw a spade in the first five attempts?
O 24%
O45%
076%
O 81%

Respuesta :

Answer:

The required probability is, 0.78

Step-by-step explanation:

There are, (52 - 13) = 39 cards which are not spade

5 cards can be chosen from the deck of 52 cards in

[tex]^{52}{C}_{5}[/tex]  ways

and out of these 5 choices, none of them will be spade in,

[tex]^{39}{C}_{5}[/tex]  ways

So,

P(None of the chosen cards is spade)

= [tex]\frac {^{39}{C}_{5}}{^{52}{C}_{5}}[/tex]

[tex]\simeq 0.22[/tex]

Hence,

P(out of these 5 choices, at least one card is spade)

[tex]\simeq (1 - 0.22)[/tex]

= 0.78

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