Which of these situations fit the conditions for using Bernoulli trials? Explain

Question

Which of these situations fit the conditions for using Bernoulli trials? Explain a) You are rolling 8 dice and need to get at least two 6s to win the game b) We record the distribution of favorite colors of customers visiting our website c) A committee consisting of 8 men and 11 women selects a delegation of 5 to attend a professional meeting at random. What is the probability they choose all women? d) A study found that 42% of M.B A students admit to cheating A business school dean surveys all the students in the graduating class and gets responses in which cheating was admitted by 176 of 407 students a) Does each roll of one die fit the conditions for using Bernoulli trials? Chock all that apply A. No, there are more than two possible outcomes B. Yes, all the conditions are met C. No, there are two outcomes, but the probability changes with each trial D. No. multiple trials are not independent b) Does each customer of our website fit the conditions for using Bernoulli trials? Check all that apply A. Yes, all the conditions are met B. No. there are more than two possible outcomes C. No. multiple trials are not independent D. No there are two outcomes but the probability changes with each trial.

Explanation / Answer

Solution:

Bernoulli trial isan experiment where we have exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

a). You are rolling 8 dice and need atleast 2 sixes to win the game.

We have two possible out comes in each roll of the die, either we get a six or not, i.e either we have a success or failure. All 8 dice have same probablilty of giving a six. So this is a Bernoulli trial as all the conditions are met.

b). We record the distribution of favourite colors of customers visiting our website.

No, We have thousands of colors and each choice can have different probability, so there are more than two possible outcomes.

c) A commitee consisting of 8 men and 11 women selects a delegation of 5. what is the probability they select all women.

This is a question of probaility not choices, we have number of ways we can select 5 women from 11 women. So no there are more than 2 possible outcomes.

d). Yes, we have 407 students and each student has only two outcomes, either he cheats or not, which is success or failure. So each student fit the condition for using bernoulli trials.

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