Question

Ch6 Q7

An Olympic archer misses the​ bull's-eye 11​% of the time. Assume each shot is independent of the others. If she shoots 9 ​arrows, what is the probability of each of the results described in parts a through f​ below?

​

a) Her first miss comes on the third arrow.

The probability is __________________

​(Round to four decimal places as​ needed.)

​

b) She misses the​ bull's-eye at least once.

The probability is __________________

​(Round to four decimal places as​ needed.)

​

c) Her first miss comes on the second or third arrow.

The probability is _________________

​(Round to four decimal places as​ needed.)

​

d) She misses the​ bull's-eye exactly 3 times.

The probability is __________________

​(Round to four decimal places as​ needed.)

​

e) She misses the​ bull's-eye at least 3 times.

The probability is ______________

​(Round to four decimal places as​ needed.)

​

f) She misses the​ bull's-eye at most 3 times.

The probability is ______________

​(Round to four decimal places as​ needed.)

Please show all of the math please because I use it as an aid for future problems. Thank you

Answer 1

a)

Her first miss comes on the third arrow =(1-0.11)²*0.11=0.0871

b) She misses the​ bull's-eye at least once =1-(0.89)⁹ =0.6496

c) Her first miss comes on the second or third arrow =0.89*0.11+0.89²*0.11 =0.1850

d) She misses the​ bull's-eye exactly 3 times =⁹C₃(0.11)³(0.89)⁶ =0.0556

e) She misses the​ bull's-eye at least 3 times =P(X>=3)=1-P(X<=2)=1-(P(X=0)+P(X=1)+P(X=2))=0.0672

f)

She misses the​ bull's-eye at most 3 times. The probability is =P(X<=3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=0.9883