Multiplication Rule for Independent Events in Statistics

Question

Calculate each probability.

First Question: Suppose you draw two cards out of a standard deck with replacement. What is the probability that one of the cards is a jack and the other is a club?

Second Questions: On awards day at the end of the year, Jasmine has an 85% chance of winning the top award in English and a 4 out of 5 chance of winning an award for athletics. Whats the probability that Jasmine wins both awards?

Answer 1

Q1: Since we're sampling with replacement, the first and second cards chosen are independent--that is, whichever card is selected first has no impact on the card selected second. So P(one jack and one club) = P(one jack) x P(one club) = (13 / 52) x (13 / 52) = (1/4) x (1/4) = 1/16

Q2: Assuming that the awards are independent (so winning the top award in English has no impact on whether Jasmine wins the top award in athletics, and vice versa), P(winning both) = P(winning English) x P(winning athletics) = 0.85 x (4/5) = 0.85 x 0.8 = 0.68.