An event has a probability of 20% of occurring. Given 10 trials, what is the probability of it occurring more than 6 times.

Question

BlackTom AI · Accepted Answer

We start by restating the problem in our own terms to ensure clarity: we have a binomial scenario with n = 10 trials and success probability p = 0.2 per trial, and we want P(K > 6), where K is the number of successes.
Option A: 'Binomial(k=6, n=10, p=.2, Cumulative=FALSE' This expression would represent the probability of exactly 6 successes, i.e., P(K = 6). It does not give the probability of more than 6 successes, so it is not appropriate for P(K > 6).
Option B: 'Binomial(k=6, n=10, p=.2, Cumulative=TRUE)' This gives the cumulative probability P(K ≤ 6). While this is a related quantity, on its own it does not equal P(K > 6); we would need to transform it further to obtain the > 6 probability.
Option C: '1- Binomial(k=6, n=10, p=.2, Cumulative=FALSE)' Here we have 1 minus the probability of exactly 6 successes, i.e., 1 - P(K = 6). This does not correspond to P(K > 6); subtracting the single-point probability does not account for the probabilities of 7, 8, 9, or 10 successes.
Option D: '1- Binomial(k=6, n=10, p=.2, Cumulative=TRUE)' This expresses 1 minus the cumulative probability up to 6, i.e., 1 - P(K ≤ 6). Since P(K > 6) equals P(K ≥ 7), and P(K ≤ 6) + P(K ≥ 7) = 1 in a binary count, this formula correctly yields the probability of observing more than 6 successes.
To connect to the underlying math: the binomial distribution gives P(K ≤ 6) as the sum of P(K = k) for k = 0 to 6. Therefore 1 - P(K ≤ 6) sums over k = 7 to 10, which is exactly P(K > 6). The other options fail because they either target a single outcome (k = 6) or misrepresent the relationship between cumulative and complementary probabilities.
In summary, the expression that computes the probability of more than 6 successes by removing the cumulative up to 6 from 1 is the one labeled with a 1 minus a cumulative probability up to 6.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 10. Quiz for Class 10

An event has a probability of 20% of occurring. Given 10 trials, what is the probability of it occurring more than 6 times.

查看解析

登录即可查看完整答案

类似问题

Which of the following situations describes a binomial random variable?

An Olympic archer has a 89% chance of hitting a bullseye on a shot. If this archer attempts 6 shots at the target, which of the following is the correct way to calculate the probability of hitting the bullseye no more than four times? Assume all conditions of the binomial distribution are satisfied.

If p=0.6, then E[X]=10. What is the variance of X?

The probability of only 2 possible outcomes - For instances- a student randomly guessing the answers to 25 multiple-choice is the example of

If x is a binomial random variable with n =8 and p =0.6, the mean value of x is

位置8的问题 In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is _____.10526

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单