A company is conducting a sweepstakes,and ships two boxes of game pieces to a particular store.4% of the contents of box A are winners,while 6% of the contents of box B are winners.Box A contains 36% 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)0.05
C)0.053
D)0.04
E)0.014

Question

Quizplus · Accepted Answer

Let's say box A has x tickets and box B has y tickets. Then we know:
x + y = 100% (Total tickets)
0.04x = number of winning tickets in box A
0.06y = number of winning tickets in box B
0.36x = percentage of tickets in box A
From the last equation, x = 0.36y
Substituting x in the first equation: 0.36y + y = 100
1.36y = 100
y = 73.53
x = 26.47

Now we can find the total number of winning tickets:
0.04(26.47) + 0.06(73.53) = 0.053

So the probability of choosing a winning ticket is 0.053.

A Company Is Conducting a Sweepstakes,and Ships Two Boxes of Game