Gallant has a subscription to "free coffee" at Soakin’ Bagels, but he still often tips the employees. (Goofus pays full price for coffee and does not tip.) If he doesn’t tip it's usually because he doesn’t have any $1 bills on hand. The following table gives the pmf of $X$, Gallant’s tip each time he goes to Soakin’ Bagels. **Table 10.5.2** \[ \begin{array}{|c|c|c|c|c|} \hline x & \$0 & \$1 & \$2 & \$3 \\ \hline P[X = x] & 0.1 & 0.5 & 0.35 & 0.05 \\ \hline \end{array} \] a. Verify that the above pmf is indeed a pmf. b. What is the probability that Gallant tips? c. What is the average value of Gallant’s tip each morning? --- Suppose 100 electronic parts are randomly sampled. It is known that these electronic parts have a 3% failure rate. Let $Y$ represent the number of defective parts in the sample of 100. a. What is the probability that exactly 5 parts in the sample are defective? Make sure that the correct formula for the answer is included in your response. b. What is the expected number of defective parts in the sample? Give an exact answer.

Gallant has a subscription to "free coffee" at Soakin’ Bagels, but he still often tips the employees. (Goofus pays full price for coffee and does not tip.) If he doesn’t tip it's usually because he doesn’t have any $1 bills on hand. The following table gives the pmf of $X$, Gallant’s tip each time he goes to Soakin’ Bagels. Table 10.5.2 \[ \begin{array}{|c|c|c|c|c|} \hline x & \$0 & \$1 & \$2 & \$3 \\ \hline P[X = x] & 0.1 & 0.5 & 0.35 & 0.05 \\ \hline \end{array} \] a. Verify that the above pmf is indeed a pmf. b. What is the probability that Gallant tips? c. What is the average value of Gallant’s tip each morning? --- Suppose 100 electronic parts are randomly sampled. It is known that these electronic parts have a 3% failure rate. Let $Y$ represent the number of defective parts in the sample of 100. a. What is the probability that exactly 5 parts in the sample are defective? Make sure that the correct formula for the answer is included in your response. b. What is the expected number of defective parts in the sample? Give an exact answer.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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