Solve the problem. Round to four decimal places.
-According to a recent study, 1 in every 7 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked
Each whether she has been a victim of domestic abuse at some point in her life. Find the probability
That at least 2 of the women sampled have been the victim of domestic abuse. Round to six decimal
Places.
A)0.713804
B)0.109532
C)0.176664
D)0.890468

Question

Quizplus · Accepted Answer

To find the probability that at least 2 of the 25 women sampled have been victims of domestic abuse, it's easier to calculate the complement: the probability that either none or only one woman has been a victim, and then subtract this from 1. Given the probability of being a victim is 1/7, the probability of not being a victim is 6/7. For zero victims, the probability is $(6/7)^{25}$. For exactly one victim, it's $25 \times (1/7) \times (6/7)^{24}$. The sum of these probabilities gives the chance of having 0 or 1 victims, and subtracting this sum from 1 gives the probability of having at least 2 victims. Calculating this yields a result closest to option D when rounded to six decimal places.

Solve the Problem. Round to Four Decimal Places