Probability Tree and Combinations

Question

A committee of four is selected from a total of 4 freshman, 5 sophomores, and 6 juniors . Find the probability of the following events:

a. Atleast 3 freshman

b. All 4of the same class

c. Not all 4 from the same class

d. Exactly 3 of the same class

Answer 1

(a)

A committee of four is selected from a total of 4 freshman, 5 sophomores, and 6 juniors.

Find the probability of the event that committee consisting atleast 3 freshman.

Atleast 3 freshman refers to committee can have 3 or 4 freshman.

Number of selections for committee having atleast 3 freshman is .

Total number of ways of selecting 4 members is .

Number of combinations for committee having atleast 3 freshman is 45.

Probability.

.

The probability that the committee has atleast 3 freshman is 0.03.

Answer 2

(b)

Find the probability that the committee consists of all four of them from the same class.

Number of ways of selecting a committee having all four of them from the same class is .

Total number of ways of selecting 4 members is .

Probability.

The probability that committe having all four of them from the same class is 0.015.

Answer 3

(c)

Find the probability that the committee having not all four of them from the same class.

Probability.

From (b), probability that committe having  all four of them from the same class is 0.015.

Probability that committe having not all four of them from the same class is 0.985. 

Answer 4

(d)

Find the probability that the committee consisting exactly 3 of them from the same class.

Exactly 3 of them are of same class refers to only  3 are of them from the same class and 1 from other class.

Total number of ways of selecting 4 members is .

Number of selections for committee having exactly 3 of them from the same class is .

Probability

Probability that the committee consisting exactly 3 of them from the same class is 0.23.