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AQA GCSE · Question 05.2 · Probability
A left-handed student is chosen at random. Work out the probability that the student wears glasses.
A left-handed student is chosen at random. Work out the probability that the student wears glasses.
How to approach this question
This is a conditional probability question. The condition is that the student is left-handed. First, find the total number of left-handed students from your Venn diagram. This will be the denominator of your fraction. Then, find the number of left-handed students who wear glasses. This will be the numerator.
Full Answer
From the Venn diagram, the total number of left-handed students is the sum of those in the L circle: 7 (wears glasses) + 15 (doesn't wear glasses) = 22.
The number of left-handed students who also wear glasses is 7 (the intersection).
The probability is the number of favourable outcomes divided by the total number of possible outcomes.
P(wears glasses | is left-handed) = 7 / 22.
This question asks for a conditional probability. We are given the condition that the chosen student is left-handed.
From the Venn diagram, the total number of left-handed students is the sum of the numbers in the "L" circle: 7 + 15 = 22. This is our sample space, so it's the denominator of the probability fraction.
We want to find the probability that this student wears glasses. Looking at the left-handed students, 7 of them wear glasses. This is our number of successful outcomes, so it's the numerator.
Therefore, the probability is 7/22.
Common mistakes
✗ Using the total number of students (78) as the denominator, giving 7/78.
✗ Using the total number of students who wear glasses (28) as the denominator.
✗ Giving the answer as a ratio 7:22 instead of a fraction.
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