Question

75% of all people enjoy sports. Everyone else doesn't.Let the

random varible X be the number who doesn't enjoy sportamong 7
randomly selected persons.
- Find the probability that no more than 6 of the 7do not
enjoy sports?

Answer 1

Answer: The probability that no more than 6 of the 7 do not enjoy sports = 0.9999.

Explanation:

Given : The proportion of people enjoy sports : p= 0.75

So , the proportion of people doesn't enjoy sports = 1-0.75=0.25

Let the random variable X be the number who doesn't enjoy .

Total number of people randomly selected : n= 7

Using Binomial distribution , the probability of getting x success :

`P(X)=^nC_xp^x(1-p)^(n-x)` , n= Number of trails , p= Probability of getting success in each trial.

The probability that no more than 6 of the 7 do not enjoy sports :

`P(X)=[tex]P(x\leq6)=1-P(x<6)\\\\=1-P(x=7)\\\\=1-^(7)C_7(0.25)^7(1-0.25)^(0)\\\\=1-(1)(0.25)^7\\\\=1-0.00006103515625=0.999938964844\approx0.9999`

Hence, the probability that no more than 6 of the 7 do not enjoy sports = 0.9999 .