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
