Question

According to a survey, 15% of city workers take the bus to work. Donatello randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work

0.001
0.002
0.128
0.900

Answer 1

A. .001

Explanation:

i got it right

Answer 2

0.001

Explanation:

Given:

Total number of workers,
`n=10`.

Number of workers taking bus,
`x=6`

Let the probability of taking bus be success and denoted by
`p`.

So,
`p=0.15`

Therefore, probability of not taking bus,
`q=1-p=1-0.15=0.85`

Using Bernoulli's distribution of getting
`x` successes out of
`n` trials.

∴
`P(X=x)=_(x)^(n)\textrm{C}p^(x)q^(n-x)`

Plug in 0.15 for
`p`, 0.85 for
`q`, 10 for
`n` and 6 for
`x`

So,
`P(X=6)=_(6)^(10)\textrm{C}(0.15)^(6)(0.85)^(10-6)\\ P(X=6)=_(6)^(10)\textrm{C}(0.15)^(6)(0.85)^(4)\\ P(X=6)=0.001`

Therefore, the probability that exactly 6 workers take bus is 0.001.