Foundation June 2023 Paper 3 Q9

OCRFoundationCurrent spec5 marksBasic ProbabilitySets

9 \(\mathscr{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}\)
\(\text{T} = \{2, 4, 6, 8, 10, 12\}\)
\(\text{F} = \{5, 10\}\)

(a) The elements 1 and 2 have been entered on this Venn diagram.

Complete the Venn diagram to show all of the elements.

Venn diagram with overlapping sets T and F inside the universal set; 2 is in T only and 1 is outside both sets

[2]

(b) Finley picks one of the 13 elements in the universal set, \(\mathscr{E}\), at random.

Write down the probability that the element is a member of both set T and set F. [1]

(c) Sam picks one of the 13 elements in the universal set, \(\mathscr{E}\), at random.

Sam says

The probability the element is in set T is \(\dfrac{6}{13}\).

The probability the element is in set F is \(\dfrac{2}{13}\).

Therefore, the probability the element is in set T or set F is \(\dfrac{6}{13} + \dfrac{2}{13} = \dfrac{8}{13}\).

Sam is wrong.

Explain Sam’s error and give the correct answer. [2]

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