Consider the 12 face cards from a deck of playing cards (king, queen, and jack). Ben draws three cards from these face cards with replacement. What it the probability that he draws at least one Jack?
A) 1.7%
B) 70.4%
C) 8.3%
D) 15%

Question

Quizplus · Accepted Answer

The easiest way to solve this problem is by calculating the probability of the complementary event (not drawing any Jacks) and subtracting it from 1. Since there are 12 face cards and 4 of them are Jacks, there are 8 cards that are not Jacks. The probability of drawing a non-Jack card three times in a row, with replacement, is (8/12)^3 = (2/3)^3 = 8/27. Therefore, the probability of drawing at least one Jack is 1 - 8/27 = 19/27, which is approximately 70.4%.

Consider the 12 Face Cards from a Deck of Playing