Question

According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work? Round the answer to the nearest thousandth.

0.001

0.002

0.128

0.900

Answer 1

Answer:0.001

x=the number of workers taking the bus to work

p= probability of success =(15/100) = 0.15

q= probability of failure =1- p = 0.85

P(X=6) = 10C6(0.15)^6(0.85)^4

= 0.001

Answer 2

Answer: 0.001

Explanation:

Binomial probability formula :

`P(x)=^nC_xp^x(1-p)^(n-x)`, where P(x) is the probability of exactly x successes in n trials.

Given : The probability of city workers take the bus to work =15%=0.15

The sample size :n= 10

Now, the probability that exactly 6 put of 10 workers take the bus to work :-

`P(6)=^(10)C_6(0.15)^(6)(1-0.15)^(10-6)\\\\=(10!)/(6!(10-6)!)(0.15)^6(0.85)^4\\\\=0.0012486552627\approx0.001`

Therefore , the probability that exactly 6 workers take the bus to work = 0.001