There are 20 identical looking packets of white powder. 8 of them contain cocaine and 12 do not. Four of the packets are randomly selected. Let X equal the number of the selected packets which contain cocaine. a. How many possible ways are there to select the 4 out of 20 packets (order does not matter) without replacement? b. What is the probability that X = 0 c. What is the probability that X=4?

There are 20 identical looking packets of white powder. 8 of them contain cocaine and 12 do not. Four of the packets are randomly selected. Let X equal the number of the selected packets which contain cocaine. a. How many possible ways are there to select the 4 out of 20 packets (order does not matter) without replacement? b. What is the probability that X = 0 c. What is the probability that X=4?

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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Question

**Problem Statement:**

There are 20 identical looking packets of white powder. 8 of them contain cocaine and 12 do not. Four of the packets are randomly selected. Let $ X $ equal the number of the selected packets which contain cocaine.

**Questions:**

a. How many possible ways are there to select the 4 out of 20 packets (order does not matter) without replacement?
b. What is the probability that $ X = 0 $?
c. What is the probability that $ X = 4 $?
d. What is the probability that $ X > 3 $?
e. What is the expected value of $ X $?
f. What is the standard deviation of $ X $?
g. What is the probability that $ X $ is smaller than its expected value?
h. What is the probability that $ X = 5 $?

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7.
DETAILS
a. How many possible ways are there to select the 4 out of 20 packets (order does not matter) without replacement?
b. What is the probability that X = 0
c. What is the probability that X=4?
d. What is the probability that X > 3?
e. What is the expected value of X?
f. What is the standard deviation of X?
MY NOTES
There are 20 identical looking packets of white powder. 8 of them contain cocaine and 12 do not. Four of the packets are randomly selected. Let X equal the number of the selected packets which
contain cocaine.
g. What is the probability that X is smaller than its expected value?
h. What is the probability that X = 5?
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