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

Answer:

0.001

Step-by-step 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.