Question

A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the number of defective sets purchased by the hotel, find the probability distribution of X. Express the results graphically as a probability histogram.

Answer 1

Answer:

The probability distribution is

X    :        0              1                 2

f(X) :       2/7          4/7               1/7

Step-by-step explanation:

Let x is the number of defective sets purchased by the hotel.

Total number of television sets = 7

Total number of defective television sets = 2

Since there are 2 defective television sets and hotel purchase 3 sets, So, X=0,1,2.

If X=0,

$P(X=0)=\frac{^5C_3}{^7C_3}=\frac{10}{35}=\frac{2}{7}$

If X=1,

$P(X=1)=\frac{^5C_2\cdot ^2C_1}{^7C_3}=\frac{10\cdot 2}{35}=\frac{4}{7}$

If X=2,

$P(X=2)=\frac{^5C_1\cdot ^2C_2}{^7C_3}=\frac{5\cdot 1}{35}=\frac{1}{7}$

The probability distribution is

X    :        0              1                 2

f(X) :       2/7          4/7               1/7

The probability histogram is shown below.