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

Question

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

Answer 1

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: $p_1=\frac{4}{52}=\frac{1}{13}.$ The probability that a card is a king is: $p_2=\frac{4}{52}=\frac{1}{13}$ and the probability we get a heart: $p_3=\frac{1}{4}$. As a result, we get: $p=p_1\cdot p_2\cdot p_3=\frac{1}{13}\cdot\frac{1}{13}\cdot\frac{1}{4}\approx0.0015$

Answer: 0.0015