IB Maths AI SL AI 4.3 Probability and distributions questions

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Question 1

Paper 2Medium6 marks

Two independent fair spinners are used in a game. Spinner $X$ has four equally likely results, $1,2,3,4$ and spinner $Y$ has five equally likely results, $1,2,3,4,5$ The outcome of a round is the ordered pair $(X,Y)$ The table shows the sum for each possible outcome.

$X\backslash Y$	1	2	3	4	5
1	2	3	4	5	6
2	3	4	5	6	7
3	4	5	6	7	8
4	5	6	7	8	9

Let $E$ be the event that the sum is at least 7.

(a)

Find the theoretical probability of $E$

[2]

(b)

Find the probability of the complementary event $E'$

[1]

(c)

Find the expected number of rounds in which $E$ occurs in 80 rounds.

[1]

(d)

In a trial of 80 rounds, $E$ occurs 21 times. Find the relative frequency of $E$

[1]

(e)

Does this trial prove that the spinners are not fair? Give a reason.

[1]

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