Answer to Question #152562 in Statistics and Probability for Daniel

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

$$P=P(5)P(Heart)P(King)=\dfrac{4}{52}(\dfrac{13}{52})(\dfrac{4}{52})$$

$$=\dfrac{1}{13}(\dfrac{1}{4})(\dfrac{1}{13})=\dfrac{1}{676}$$

If the order is important

$$P=\dfrac{1}{676}\approx0.0015$$

If the order is not important, there are 6 possible variants

$$3!=6$$ $$(5, H, K), (5, K, H), (H, 5, K), (H,K,5),$$

$$(K,5,H),(K,H,5)$$

$$P=6(\dfrac{1}{676})=\dfrac{3}{338}\approx0.0089$$

c. 0.0015