In one city,the probability that a person will pass his or her driving test on the first attempt is 0.68.11 people are selected at random from among those taking their driving test for the first time.What is the probability that among these 11 people,the number passing the test is between 2 and 4 inclusive?
A)0.0057
B)0.0345
C)0.0299
D)0.0251
E)0.0308

Question

Quizplus · Accepted Answer

This is a binomial probability problem where $n = 11$, $p = 0.68$ (probability of success), and $q = 1 - p = 0.32$ (probability of failure). We are looking for the probability of $k$ successes (passing the test) where $k$ is between 2 and 4 inclusive. The binomial probability formula is $P(X = k) = \binom{n}{k}p^kq^{n-k}$.To find the probability that between 2 and 4 people (inclusive) pass the test, we calculate the probabilities for exactly 2, 3, and 4 people passing and sum them up:- For $k = 2$: $P(X = 2) = \binom{11}{2}(0.68)^2(0.32)^9$- For $k = 3$: $P(X = 3) = \binom{11}{3}(0.68)^3(0.32)^8$- For $k = 4$: $P(X = 4) = \binom{11}{4}(0.68)^4(0.32)^7$Summing these probabilities gives the total probability of having between 2 and 4 people passing the test. The correct answer is calculated by performing these operations, which matches with option E, indicating that the sum of these probabilities equals 0.0308. This calculation involves using the binomial coefficients and the given probabilities to compute each scenario's probability and then summing them for the final answer.

In One City,the Probability That a Person Will Pass His