Question

A bag contains 10 white and 3 black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw?

Options

• `15/286`

• `1/286`

• `1/281`

• `1/211`

Answer 1

`15/286`

Explanation:

Out of the 3 black balls 2 should have been drawn in the first six draws so that when the third appears in the seventh draw the procedure ends.

In the first six draws 4 white balls and 2 black balls should have been drawn so that the required probability

= `""^6C_4 10/13. 9/12. 8/11. 7/10. 3/9. 2/8. 1/7 = 15/286`