Edexcel S1 — Question 5

Exam BoardEdexcel
ModuleS1 (Statistics 1)
TopicDiscrete Probability Distributions
TypeSum or product of two independent values
  1. Two spinners are in the form of an equilateral triangle, whose three regions are labelled 1,2 and 3, and a square, whose four regions are labelled \(1,2,3\) and 4 . Both spinners are biased and the probability distributions for the scores \(X\) and \(Y\) obtained when they are spun are respectively:
\(x\)123
\(\mathrm { P } ( X = x )\)\(0 \cdot 2\)\(0 \cdot 4\)\(p\)
\(Y\)1234
\(\mathrm { P } ( Y = y )\)0.20.5\(q\)\(q\)
  1. Find the values of \(p\) and \(q\).
  2. Find the probability that, when the two spinners are spun together, the sum of the two scores is (i) 5, (ii) less than 4 .
  3. State an assumption that you have made in answering part (b) and explain why it is likely to be justifiable.
  4. Calculate \(\mathrm { E } ( X + Y )\).
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