Question

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%

Answer 1

the answer would be c. 42.2 percent

Answer 2

The correct answer is C. 42.2%

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

`\text{Probability that she does not get a spade in first draw = }(39)/(52)`

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

`\text{So, Probability that she does not get a spade in second draw = }(39)/(52)`

`\text{Similarly, Probability that she does not get a spade in third draw = }(39)/(52)`

`\text{Thus, Probability that she will lose the game = }(39^3)/(52^3)=0.422`

`\text{Also, The percentage of Probability that she will lose the game = }0.422* 100=42.2\%`

Hence, The correct answer is C. 42.2%