Question

Julia enjoys shooting paper balls into the wastebasket across her office. She misses the first shot 50% of the time. When she misses on the first shot, she misses the second shot 20% of the time. What is the probability of missing two shots in a row? (10 points)

Would the answer be .4

Answer 1

The probability of missing on the first shot is 0.5. The probability of missing on the second shot, having missed on the first shot, is 0.2. Therefore the probability of missing two shots in a row is:

`P(2\ misses\ in\ a\ row)=0.5*0.2=0.1`

Answer 2

Answer: Probability of missing two shots in a row is 10% of the time.

Explanation:

Since we have given that

Probability of missing the first shot = 50% of the time

P(A) = 50%

(Here, A denotes the event of missing the first shot)

Let B be the event missing the second shot .

Probability of missing the first shot, she misses the second shot = P(B|A)= 20% of the time.

Probability of missing two shots in a row is given by P(A∩B)

`P(B\mid A)=(P(A\cap B))/(P(A))\\\\0.2=(P(A\cap B))/(0.5)\\\\0.2* 0.5=P(A\cap B)\\\\0.10=P(A\cap B)\\\\0.10* 100\%=P(A\cap B)\\\\10\%=P(A\cap B)`

Hence, Probability of missing two shots in a row is 10% of the time.