Question

Shipment of 7 television sets contains 3 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

The number of possible ways to pick up 3 sets from 7 is $7\cdot6\cdot5=210$. Suppose that we want to pick up 1 defective set and two normal. The number of possible choices is: $3\cdot4\cdot3=36$, In case we want to collect 2 defective sets and 1 normal, the probability is: $3\cdot2\cdot4=24$. In case we want to pick up 3 defective sets, we can make it in $3\cdot2\cdot1=6$ ways. In case we want to take 3 normal sets, we can make it in $4\cdot3\cdot2=24$ ways. Thus, we get: $P(X=0)=\frac{24}{210}$, $P(X=1)=\frac{36}{210}$, $P(X=2)=\frac{24}{210}$ , $P(X=3)=\frac{6}{210}$ .