Question

63​% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answer 1

Answer:

a. 0.00069

b. 0.063

c.0.00095

Step-by-step explanation:

a. Probability that exactly 5 men consider themselves professional baseball fans:-

Here, there's a 63/100 or 63% possiblity that five (5) men consider themselves fans and of course, a 37/100 possibility that the other 5 men consider themselves non fans. Each of these must be multiplied and then the result will be the probability that exactly five men consider themselves baseball fans:-

(63/100)^5 × (37/100)^5

= 0.09924 × 0.006934

= 0.000688

Therefore the probability that 5 consider themselves baseball fans is 0.00069

b. The probability that at least 6 are fans:-

In this case, each of the 6 men have some 63/100 or 63% possibility of being a fan.

We therefore multiply 63/100 by itself up to six times

i.e 63/100 × 63/100 × 63/100 × 63/100 × 63/100 × 63/100

or (63/100)^6

= 0.06252

The probability that at least 6 men consider themselves professional baseball fans is 0.063

c. Probability that less than four consider themselves baseball fans:-

In this scenario, it means that at least 7 men out of the ten do not consider themselves professional baseball fans. We then simply multiply 37/100 by itself up to seven times. It isn't too necessary what the remaining three are.

= (37/100)^7

= 0.0009493

Therefore the possibility that less than four men do not consider themselves baseball fans is 0.00095