Question

1. There are 9 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible?

60,480
720
84
531,441

2. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

16

3. A pitching machine throws 70% strikes and 30% balls. Five pitches will be thrown by the machine.
What is the probability the machine will throw one ball and four strikes?

0.3 × 0.7⁴

0.3 + 4 × 0.7

5 × 0.3 × 0.7⁴

none of these

4. Suppose that A, B are two independent events, with P(A) = 0.1 and P(B) = 0.2.
Find P(A or B).

0.15

0.02

0.30

0.28

Answer 1

Q1) The number of different subcommittee of 6 members that can be formed from the 9 members on board is computed here as number of ways to select 6 members from 9 members

Q2) There are a total of 3*4 = 12 face cards and four cards of number 5. Therefore a total of 16 cards could be selected here. Therefore the probability here is computed as:

= 16/52

= 0.3077

Therefore 0.3077 is the required probability here.

Q3) The number of strikes out of the 5 pitches is modelled here as a binomial distribution given as:

as the probability of a strike is 0.7.

Now the required probability here is computed as:

Therefore C is the correct answer here.

Q4) We are given here that:
P(A) = 0.1, and P(B) = 0.2

For independent events, P(A and B) = P(A)P(B) = 0.1*0.2 = 0.02

Using law of addition of probability, we have here:
P(A or B) = P(A) + P(B) - P(A and B) = 0.1 + 0.2 - 0.02 = 0.28

Therefore 0.28 is the required probability here.