An M&Ms bag contains only 7 red M&Ms and 5 blue M&Ms. You will draw 3 M&Ms from

Question

An M&Ms bag contains only 7 red M&Ms and 5 blue M&Ms. You will draw 3 M&Ms from the bag. If you select 2 or more blue M&Ms you throw away the whole bag. Otherwise, you finish the bag.

1- Define the experiment for this game and the pertinent random variable (X)

2- Fully specify the PMF for the RV defined in question1.

3-Fully specify the CDFfor the RV defined in question1.

4- Calculate the expected value, variance, and standard deviation of the RV defined in question 1.

5- What is the probability that you eat the whole bag?

Explanation / Answer

1.) The random variable (X) for the experiment is the number of blue M&Ms withdrawn from the bag.

X = {0,1,2,3}

It can take above mentioned 4 values.

2.) THe probability mass funciton.

P(X=0) = P(O Blue 3 White)

= (5C0 * 7C3 ) / 12C3

= 0.159

Similarly, we can calculate other probabilities also.

3.) Summing the Probability mass function sequentially gives cumulative distribution function.

4.) E(x) = px

= (0.159 * 0) + (0.477 * 1) + (0.318 * 2) + (0.045 * 3)

= 1.25

Variance = E(x2) - (E(x))2

E(x2) = px2

   = 2.15 - 1.5625

Variance = 0.596

Standard Deviation = Variance

= 0.596

= 0.772

5.) Probability of eating the whole bag = P(X=0) + P(X=1) or P(X < 2)

= 0.159 + 0.477

= 0.636

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