gmatruler wrote:Joshua and jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
A) 1/15
B) 1/12
C) 1/9
D) 1/6
E) 1/3
We also could handle this as a straight probability question.
Probability = (good outcomes)/(total outcomes)
In this problem:
good outcome = Josh or Jose
total outcomes = total number of people
Probability of picking Josh or Jose on the first pick:
2/6 (because there are 2 good outcomes out of a total of 6 people)
Probability of picking Josh or Jose on the second pick:
1/5 (because if Josh or Jose was chosen on the first pick, then only 1 good outcome is left for the 2nd pick, out of a total of 5 remaining people)
We need both of these events to happen. When we want multiple events to happen, we multiply the fractions:
P(A and B) = P(A) * P(B)
We multiply the fractions because the more events we want to happen together, the smaller the probability, and when we multiply fractions, the result just keeps getting
smaller.
2/6 * 1/5 = 2/30 = 1/15.
The correct answer is A.
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