Answer:
a) 2.60x10^-7
b) 5.31x10^-5
c) 2.19x10^-3
Step-by-step explanation:
X=number of hits
The probability is the number of desired outcomes divided by the total number of all outcomes.
Then
a) P(X=6)=P({1, 1, 1, 1, 1, 1})=6/40*5/39*4/38*3/37*2/36*1/35=2.60x10^-7
b) P(X=5)=P({0, 1, 1, 1, 1, 1})+P({1, 0, 1, 1, 1, 1})+...+P({1, 1, 1, 1, 1, 0}), every one of these have the same probability
P(X=5)=6P({1, 1, 1, 1, 1, 0})=6*(6/40*5/39*4/38*3/37*2/36*34/35)=5.31x10^-5
c) P(X=4)=P({0, 0, 1, 1, 1, 1})+...+P({1, 1, 1, 1, 0, 0}) every one of these have the same probability.
![P(X=4)=(^6_4)P({1, 1, 1, 1, 0, 0})=\frac{6!}{4!(6-4)!}(\frac{6}{40} \frac{5}{39} \frac{4}{38} \frac{3}{37} \frac{34}{36} \frac{33}{35} )=2.19\times 10^{-3}](https://tex.z-dn.net/?f=P%28X%3D4%29%3D%28%5E6_4%29P%28%7B1%2C%201%2C%201%2C%201%2C%200%2C%200%7D%29%3D%5Cfrac%7B6%21%7D%7B4%21%286-4%29%21%7D%28%5Cfrac%7B6%7D%7B40%7D%20%5Cfrac%7B5%7D%7B39%7D%20%5Cfrac%7B4%7D%7B38%7D%20%5Cfrac%7B3%7D%7B37%7D%20%5Cfrac%7B34%7D%7B36%7D%20%5Cfrac%7B33%7D%7B35%7D%20%29%3D2.19%5Ctimes%2010%5E%7B-3%7D)