Find the probability the student receives exactly one scholarship.

Question

A student applies for two different scholarships. The probability of receiving the first scholarship is 0.3 and the probability of receiving the second is 0.4. The decisions are made independently.

Answer 1

Let A be the event of receiving first scholarship

Let B be the event of receiving second scholarship

The Probability of receiving first scholarship P(A) is 0.3.

The Probability of receiving second scholarship P(B) is 0.4.

The events(first scholarship and second scholarship) are independent events.

Probability of receiving first as well as second scholarship .

Two events A and B are said to be independent even then

Probability of receiving first or second scholarship .

We know that when two events are not mutually exclusive then .

Therefore the probability of student receiving only one scholarship is 0.58.

Comments

Although the work seems right, I do not have that option in my homework.

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Please provide us the options that you have.

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a.) 0.12

b.) 0.42

c.) 0.46

d.) 0.40

Answer 2

Let A be the event of receiving first scholarship

Let B be the event of receiving second scholarship

The Probability of receiving first scholarship P(A) is 0.3.

The Probability of not receiving first scholarship is 1 - P(A) = 1 - 0.3 = 0.7.

The Probability of receiving second scholarship P(B) is 0.4.

The Probability of not receiving second scholarship is = 1 - P(B) = 1 - 0.4 = 0.6

Two events A and B are said to be independent even then

Probability of receiving first as well as second scholarship = 0.3 * 0.4 = 0.12

Probability of not receiving any scholarship * = 0.7 * 0.6 = 0.42

Therefore the probability of receiving exactly one scholarship is

1 - (*) - (P(A)P(B))

= 1 - 0.42 - 0.12

= 0.46

Therefore the probability of receiving exactly one scholarship is 0.46.