The 30 students in MATH215A are invited to play “My Deal or NO DEAL!!” Each stud

waigaK

waigaK

Answered question

2021-09-15

The 30 students in MATH215A are invited to play “My Deal or NO DEAL!!” Each student will get to select one of 25 cases prior to any being opened. (It’s perfectly acceptable for two or more people to select the same case). After the cases have been selected I, as the host, will start opening the cases one by one eliminating those who didn’t select the case with the $1,000,000. If exactly 4 people selected the million dollar case, everyone will share the spoils. What is the probability that exactly 4 of you will select the correct case?

Answer & Explanation

svartmaleJ

svartmaleJ

Skilled2021-09-16Added 92 answers

Step 1
Given :
The 30 students in MATH215A are invited to play “My Deal or NO DEAL!!” Each student will get to select one of 25 cases prior to any being opened. (It’s perfectly acceptable for two or more people to select the same case). After the cases have been selected I, as the host, will start opening the cases one by one eliminating those who didn’t select the case with the $1,000,000. If exactly 4 people selected the million dollar case, everyone will share the spoils.
Play has two outcomes “My Deal or NO DEAL" and Each student will get to select one of 25 cases prior to any being opened.
Therefore, Probability of success =125=0.04
30 students in MATH215A are invited to play .
Therefore, n=30
Let, X be the number of people selected the million dollar case, everyone will share the spoils.
Here, XB(n=30,p=0.04)
Binomial probability distribution function (PDF) is given as:
P(X)=(beg{array}{c}nXend{array})pX(1p)nX
Step 2
Exactly 4 of you will select the correct case i.e. x=4:
Substitute trials =25,p=0.04,and X=4 into a binomial probability distribution function (PDF).
P(4)=30!4!(304)!0.044(10.04)304
Evaluating the expression, we have
P(X=4)=0.02427
Hence, probability that exactly 4 of you will select the correct case =0.02427

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