Question

A bag contains 4 black balls and 6 white balls. Sarah picks a ball at random from the bag and replaces it back in the bag. She then picks another ball at random from the bag.

You may draw a tree diagram on paper to answer the following questions.

Calculate the probability that she picks

a) 2 white balls or 2 black balls

Answer 1

13/25

Explanation:

number of black balls = 4

number of white balls = 6

⇒ total number of balls = 10

As the balls are always replaced after being picked:

• probability of picking a black ball = P(B) = 4/10
• probability of picking a white ball = P(W) = 6/10

Therefore,

P(W) and P(W) = 4/10 x 4/10 = 16/100 = 4/25

P(B) and P(B) = 6/10 x 6/10 = 36/100 = 9/25

P(W and W) or P(B and B) = 4/25 + 9/25 = 13/25