3. Consider an intro statistics course with 31 students. The class range from fr

Question

3. Consider an intro statistics course with 31 students. The class range from freshman through

seniors. Some students are males and some are females. There are 15 freshman students in

which 9 are female and 6 are male. There are 8 sophomore students in which 3 are females

and 5 are male. Also, there are 6 juniors in which 4 are female and 2 are male. Finally, there

are 2 seniors, 1 female and 1 male. Suppose we select one student at ransom from class.

(a) Find the probability that the student is either a freshman or a sophomore.

(b) Find the probability that the student is either a male or a sophomore.

(c) Indicate which event from part a) or b) is mutually exclusive and why?

Explanation / Answer

Male (M) Female(F)

Freshman(Fr) 6 9 15

sophomore (So) 5 3 8

juniors (J) 2 4 6

seniors (Se) 1 1 2

Total 14 17 31

A student can't be a freshman as well as sophomore or junior or senior at once. So, these all are mutually exclusive events as they can't be both at once.

So, a) part is mutually exclusive

While in the sophomore year there are some male students. So, b) is not mutually exclusive.

For a mutually exclusive event P(A U B) = P(A) + P(B),

else, P(A U B) = P(A) + P(B) - P(A n B)

a)

P(Fr) = 15/31

Number of freshman students/total strength

P(So) = 8/31

Number of Sophomores/total strength

As,it is mutually exclusive,

P(Fr U So) = 15/31 + 8/31 = 23/31

b)

P(M) = 14/31

number of males/total strength

P(So) = 8/31

number of Sophomores/total strength

P(M n So) = 5/31

Number of Male sophomores/total strength

As, it is not mutually exclusive,

P(So U M) = P(So) + P(M) - P(So n M)

=> =14/31 + 8/31 - 5/31 =17/31

c)

a) is mutually exclusive while b) is not for reasons mentioned above.

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