Question

I need help with number 7.

Answer 1

Answer:

A) 41%

Step-by-step explanation:

the complement of at least one balloon being hit is no balloons being hit

thus, if "at least one balloon is hit" is false, "no balloons are hit" is true

1 - probability something is false  = probability it is true

1 - probability no balloons are hit = probability at least one balloon is hit

probability no balloons are hit = P(A and B and C and D and E), where each event is a balloon is not hit

probability a balloon is hit = 1/10 = 0.1

probability a ballon is not hit = 1 - probability a balloon is hit = 1-0.1 = 0.9

P(A and B) = P(A) * P(B)

P(A and B and C and D and E) = 0.9*0.9*0.9*0.9*0.9 = 0.9^5 = 0.59049 = probability no balloons are hit

1 - probability no balloons are hit = probability at least one balloon is hit = 1-0.59049 = 0.40951 ≈41%