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Maria is playing a game where she is trying to draw a spade from a standard deck of cards. if she doesn't get a spade, she replaces the card, shuffles the deck, and tries again. if she draws a card 3 times and doesn't get a spade, she loses. what is the probability that maria loses the game?
A.17.8%
B.23.7%
C.42.2%
D.31.6%

Respuesta :

the answer would be c. 42.2 percent

Answer:  

The correct answer is C. 42.2%

Step-by-step explanation:

Total number of cards in the deck of playing cards = 52

Number of spades in the deck of playing cards = 13

Number of cards other than spade = 52 - 13

                                                          = 39

If she draws a card 3 times and doesn't get a spade, she loses.

So, She loses only if he gets all the three cards other than spade

[tex]\text{Probability that she does not get a spade in first draw = }\frac{39}{52}[/tex]

Now, The card is replaced if she does not get a spade.

[tex]\text{So, Probability that she does not get a spade in second draw = }\frac{39}{52}[/tex]

[tex]\text{Similarly, Probability that she does not get a spade in third draw = }\frac{39}{52}[/tex]

[tex]\text{Thus, Probability that she will lose the game = }\frac{39^3}{52^3}=0.422[/tex]

[tex]\text{Also, The percentage of Probability that she will lose the game = }0.422\times 100=42.2\%[/tex]

Hence, The correct answer is C. 42.2%

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