Mathematics, 19.07.2019 15:30 cosmicprof1

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?

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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

What is chain rule in probability?

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

$P(A \cap B) = P(B)P(A|B) = P(A)P(A|B)$

What is law of total probability?

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

$B_i \: ; i \in \{1,2,3.., n\}$

Then, suppose there is event A in sample space.

Then probability of A's occurrence can be given as

$P(A) = \sum_{i=1}^n P(A \cap B_i)$

Using the chain rule, we get

$P(A) = \sum_{i=1}^n P(A \cap B_i) = \sum_{i=1}^n P(A)P(B_i|A) = \sum_{i=1}^nP(B_i)P(A|B_i)$

For the given case, let we consider events:

A = Student randomly selected is freshmanB = Student randomly selected is sophomoreC = Student randomly selected is junior or seniorD = Student randomly selected majors in engineering.

Then, we have:

P(A) = 0.3P(B) = 0.25P(C) = 0.45P(D|A) = 0.15 (Since A had happened already(as they said student is known to be a freshmen) and then we were calculating D's probability. Its notation is P(D|A) )P(D|B) = 0.2P(D|C) = 0.3

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:

link

Answer from: merunikitty1226

Let

denote the event that a student is a freshman, L_2

a sophomore, L_3

a junior, and L_4

a senior.

Let

denote the event that a student majors in engineering. By the law of total probability,

$\mathbb P(E)=\mathbb P(E\cap L_1)+\mathbb P(E\cap L_2)+\mathbb P(E\cap L_3)+\mathbb P(E\cap L_4)$

By the definition of conditional probability, we can expand each of these intersection probabilities to get

$\mathbb P(E)=\mathbb P(E\mid L_1)\mathbb P(L_1)+\mathbb P(E\mid L_2)\mathbb P(L_2)+\mathbb P(E\mid L_3)\mathbb P(L_3)+\mathbb P(E\mid L_4)\mathbb P(L_4)$

$\mathbb P(E)=0.15\cdot0.3+0.2\cdot0.25+2(0.3\cdot0.45)=0.365$

Answer from: Quest

4400

step-by-step explanation:

Answer from: Quest

283 square feet

step-by-step explanation:

good luck

Due today (05.06)use a net to find the surface area of the right triangular prism shown below: 88

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The probability that a random student at elmville college is a freshman is 0.3; a sophomore, 0.25;...