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.
Accepted Solution
A:
Answer:The probability distribution isX : 0 1 2f(X) : 2/7 4/7 1/7Step-by-step explanation:Let x is the number of defective sets purchased by the hotel.Total number of television sets = 7Total number of defective television sets = 2Since there are 2 defective television sets and hotel purchase 3 sets, So, X=0,1,2.If X=0,[tex]P(X=0)=\frac{^5C_3}{^7C_3}=\frac{10}{35}=\frac{2}{7}[/tex]If X=1,[tex]P(X=1)=\frac{^5C_2\cdot ^2C_1}{^7C_3}=\frac{10\cdot 2}{35}=\frac{4}{7}[/tex]If X=2,[tex]P(X=2)=\frac{^5C_1\cdot ^2C_2}{^7C_3}=\frac{5\cdot 1}{35}=\frac{1}{7}[/tex]The probability distribution isX : 0 1 2f(X) : 2/7 4/7 1/7The probability histogram is shown below.