Handling Data 7
3 marks · NormalA box contains some balls. The probability that a randomly chosen ball is black is 0.2, and the probability that it is white is 0.5. The probability that it is red is unknown.
Given that the ball chosen is not black, explain how you would calculate the probability that it is white.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
0.5 divided by the probability that the ball is not black, that is 0.5 / (1 - 0.2) = 0.625
Must show: Calculation of probability of not black: 1-0.2=0.8, Division of P(white) by P(not black)
Also accept: 5/8
Common mistakes: Using 0.5 outright, ignoring the condition
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Identifies P(not black) = 1 - 0.2 = 0.8.
M2 · 1 mark · Applies conditional probability: P(white | not black) = P(white) / P(not black).
A1 · 1 mark · Obtains correct value: 0.5 / 0.8 = 0.625 (or 5/8).
Worked solution
We want to find the probability that the ball is white, given it is not black.
P(not black) = 1 - 0.2 = 0.8.
P(white | not black) = P(white) / P(not black) = 0.5 / 0.8 = 0.625 (or 5/8).