Question

Your drawer contains 6 gold earrings and 7 silver earrings. You randomly choose an earring. Without replacing the first, you choose a second earring. What is the probability that both earrings are silver

Answer 1

The probability that both earrings are silver is 0.27.

Explanation:

Basically, we have to pick in a such a way that the first earring is a silver earring and the second one is also a silver earring.

Constituents of the box= 7 silver, 6 gold.

Probability=
`(No. Of Favorable Outcomes)/(Total No. Of Outcomes)`

Therefore, probability of picking up a silver earring in the first attempt(A)=
`(7)/(13)`

As we have picked up, one earring from the bag, the no. of silver earrings have been decreased by 1 as have the total no. of earrings.

Therefore, the total no. of earrings now=12

No. of silver earrings in the bag now=6

Probability of picking up a silver in the second attempt after the above first attempt(B)=
`(6)/(12)`

P(A∩B)=P(A)*P(B)

=
`(7)/(13)` x
`(6)/(12)`

=
`(7)/(26)`

=0.269

The probability that both earrings are silver is 0.27.