Q:

The probability of picking two black marbles from a box at random without replacement is 1091 . The probability of drawing a black marble first is 514 . What is the probability of picking a second black marble, given that the first marble picked was black?

Accepted Solution

A:
The correct answer to the question above is 4/13. Below it shows how it's achieved...

EQUATION: 
P(A|B) = P(A ∩ B)
                 P(B)

Step 1: Identify 
P(B) = 5/14 
P(A ∩ B) = 10/91

Step 2: Insert into the equation and Solve
10/91 ÷ 5/14
Use reciprocal to divide
10/91 × 14/5 
Simplify the answer 
140/455
Simplified (Final Answer)
4/13