Answer to Question #152754 in Statistics and Probability for Benjamin Philip

Question #152754
Three cards are drawn randomly from a deck of cards one after the other with replacement each time. Find the probability that the three cards are a 5, a heart and a king.

a. 0.0156
b. 0.125
c. 0.0015
a. 0.0192
1
Expert's answer
2020-12-25T14:11:31-0500

We will use the Multiplication Rule (https://www.statisticshowto.com/multiplication-rule-probability/) to solve the problem. We assume that the deck has 52 cards. The probability that a drawn card is 5 is: p1=452=113.p_1=\frac{4}{52}=\frac{1}{13}. The probability that a card is a king is: p2=452=113p_2=\frac{4}{52}=\frac{1}{13} and the probability we get a heart: p3=14p_3=\frac{1}{4}. As a result, we get: p=p1p2p3=113113140.0015p=p_1\cdot p_2\cdot p_3=\frac{1}{13}\cdot\frac{1}{13}\cdot\frac{1}{4}\approx0.0015

Answer: 0.0015


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