Answer:
0.001
Step-by-step explanation:
Given:
Total number of workers, [tex]n=10[/tex].
Number of workers taking bus, [tex]x=6[/tex]
Let the probability of taking bus be success and denoted by [tex]p[/tex].
So, [tex]p=0.15[/tex]
Therefore, probability of not taking bus, [tex]q=1-p=1-0.15=0.85[/tex]
Using Bernoulli's distribution of getting [tex]x[/tex] successes out of [tex]n[/tex] trials.
∴ [tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}[/tex]
Plug in 0.15 for [tex]p[/tex], 0.85 for [tex]q[/tex], 10 for [tex]n[/tex] and 6 for [tex]x[/tex]
So, [tex]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[/tex]
Therefore, the probability that exactly 6 workers take bus is 0.001.
