Use the rule of total probability to find the indicated probability.
-A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 4% of its contents being winners, while 6% of the contents of box B are winners. Box A
Contains 34% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is
Chosen at random, what is the probability it is a winner?
A)0.1
B)0.053
C)0.05
D)0.014

Question

Use the rule of total probability to find the indicated probability.
-A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store. Box A has 4% of its contents being winners, while 6% of the contents of box B are winners. Box A
Contains 34% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is
Chosen at random, what is the probability it is a winner? 
A)0.1
B)0.053
C)0.05
D)0.014

Quizplus · Accepted Answer

The probability of picking a winner is calculated using the rule of total probability, which in this case is the sum of the probabilities of picking a winner from each box, weighted by the probability of picking from that box. For Box A, with 34% of the tickets and a 4% win rate, the contribution is 0.34 * 0.04. For Box B, with 66% of the tickets (100% - 34%) and a 6% win rate, the contribution is 0.66 * 0.06. Adding these together gives 0.0136 + 0.0396 = 0.0532, which rounds to 0.053.

Use the Rule of Total Probability to Find the Indicated