Question

There are 10 pots exposed in the shop, 2 of which have hidden defects. the customer buys two pieces. what is the probability that at least one of them has a hidden bug ?

Answer 1

Check the tree diagram, of all the possible scenarios and the probabilities.

All the possible scenarios are: 

1st.non defective,  2nd.non defective
1st.non defective,  2nd. defective
1st. defective,  2nd. non defective
1st. defective,  2nd. defective

consider the case 1st.non defective,  2nd.non defective

the probability that the first one is non defective is 8/10, since 8 out of 10 are non defective.

In this scenario, the second one is non defective as well. The probability for this to happen is 7/9, since now we have 7 non defective pots, and 9 in total.

This means that the probability of the first to be non defective, and the second non-defective is (8/10) * (7/9)=0.622

similarly we calculate the other cases, as shown in the picture.

P(at least one is defective)=
P(1st.non defective,  2nd. defective)+P(1st. defective,  2nd. non defective)+P(1st. defective,  2nd. defective)=
0.178+0.178+0.022=0.378


Answer: 0.378