Question

12. A bag has 10 marbles, and 7 are black. Petra picks 2 marbles without replacing the first. What is the probability

that both are black?

Answer 1

`(7)/(15)`

Explanation:

From the question,

The total number of marbles in the bag,n(S) =10.

The number of black marbles,n(B)=7

The probability that both marbles are red means that, the first marble is red and the second marble is red.

P(1st marble is Black)=

`(n(R))/(n(S)) = (7)/(10)`

Since Petra picked the first marble without replacing it, the total number of the marbles will reduce by 1. Same is applied to the number of black marbles.

This implies that,

P(2nd marble is black)

`=(6)/(9)`

`= (2)/(3)`

P(both are black)=

`= (7)/(10) * (2)/(3)`

`= (7)/(15)`