The probability that a random student at elmville college is a freshman is 0.3; a sophomore, 0.25; and a junior or senior, 0.45. the probability that a freshman will major in engineering is 0.15; a sophomore, 0.2; and a junior or senior, 0.3. what is the probability that a random student at this college majors in engineering?

Probability of an event is the measure of its chance of occurrence. The probability that a random student at this college majors in engineering is 0.24

For two events A and B, by chain rule, we have:

Suppose that the sample space is divided in n mutual exclusive and exhaustive events tagged as

Then, suppose there is event A in sample space.

Then probability of A's occurrence can be given as

Using the chain rule, we get

For the given case, let we consider events:

Then, we have:

The needed probability is

P(random student at this college majors in engineering) = P(D)

Using the law of total probability, we get:

P(D) = P(A).P(D|A) + P(B).P(D|B) + P(C).P(D|C)

P(D) = 0.045 + 0.06 + 0.135 = 0.24

Thus,

The probability that a random student at this college majors in engineering is 0.24

Learn more about law of total probability here:

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answer: 7

step-by-step explanation:

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