Question

. Suppose that at UVA, 76% of all undergraduates are in the College, 10% are in Engineering, 7% are in Commerce, 3% are in Nursing, and 4% are in Architecture. In each school, the per- centage of females is as follows: 55% in the College, 25% in Engineering, 49% in Commerce, 87% in Nursing, and 35% in Architecture. If a randomly selected student is male, what is the probability that he’s from the College?

Answer 1

Answer: 34.2%

Step-by-step explanation:

76% of undergrads in The College

45% of those are male (since 55% female)

.76 x .45 = 34.2% of all undergrads are males in The College

Answer 2

The probability of selecting an undergraduate student being from college and is also a male is 34.2%.

What is probability?

Probability can be defined as the chances of an event occurring, or probability helps us to know the chances of an event occurring. It is given by the formula,

$Probability = \dfrac{\text{Number of desired outcomes}}{\text{Total number of possible outcomes}}$

We know that the probability of a student going to college is 0.76(76%). And the probability of the college students being a male can be written as the probability of a college student not being a female. Also, the probability of the college student is a female is given as 0.55(55%) and the sum of all the probability of an event is 1. Thus, the probability of the college student being a male can be written as,

Probability(Male) = 1 - 0.55

                             = 0.45 = 45%

Further, the probability of selecting an undergraduate student being from college and is also a male can be written as,

$\rm Probability(Male\ College\ student) = Probabilty(College\ student) \times Probability(Male)$

$\begin{aligned}\rm Probability(Male\ College\ student) &= 0.76 \times 0.45\\&= 0.342\\&= 34.2\%\end{aligned}$

Hence, the probability of selecting an undergraduate student being from college and is also a male is 34.2%.

Learn more about Probability:

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