Question

Sophie, Ms. Coley's favorite dog, loves to play catch. The probability of Sophie catching the ball is 0.15. Ms. Coley is interested in determining how many tosses it will take for Sophie to catch the ball once. What is the probability that Sophie takes no more than 7 tosses to catch the ball?

A) 0.0347
B) .0566
C) 0.6794
D) 0.3206

Answer 1

The probability that Sophie catches the ball in no more than 7 tosses is 0.6794. This is calculated as the complement of the probability of not catching the ball across 7 tosses (1 - 0.85^7). Therefore correct option is C

Step-by-step explanation:

To determine the probability that Sophie takes no more than 7 tosses to catch the ball, we must consider the complement of the probability that Sophie does not catch the ball in 7 tosses. The probability of not catching the ball each time is 1 - 0.15, which is 0.85. Now, we need to calculate the probability that she does not catch the ball in all 7 attempts and subtract that from 1. This uses the concept of geometric distribution in probability.

The mathematical expression is:

1 - (Probability of not catching)^number of tosses

So for not catching the ball in 7 tosses:

1 - 0.85^7

Calculating this gives us:

1 - 0.85^7 ≈ 0.6794

Therefore, the correct answer is C) 0.6794, which represents the probability that Sophie catches the ball in no more than 7 tosses.