At an eastern state's university,60% of the students are from suburban areas,30% are from rural areas,and 10% are from urban areas.Of the students from the suburban areas,60% are nonbusiness majors.Of the students from the rural areas,70% are nonbusiness majors.Of the students from the urban areas,90% are nonbusiness majors.
-The probability that a randomly selected student is a business major is ________.

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected student is a business major, we can use the law of total probability and consider the probabilities from each area:

P(business major) = P(suburban area) * P(business major|suburban) + P(rural area) * P(business major|rural) + P(urban area) * P(business major|urban)

Substituting in the given probabilities, we get:

P(business major) = 0.6 * 0.4 + 0.3 * 0.3 + 0.1 * 0.1
P(business major) = 0.24 + 0.09 + 0.01
P(business major) = 0.34

Therefore, the probability is 0.34 or choice C.

At an Eastern State's University,60% of the Students Are from Suburban