OCR PURE — Question 13

Exam BoardOCR
ModulePURE
TopicDiscrete Probability Distributions
TypeComparison or ordering of two independent values

13
  1. The probability distribution of a random variable \(X\) is shown in the table, where \(p\) is a constant.
    \(x\)0123
    \(P ( X = x )\)\(\frac { 1 } { 12 }\)\(\frac { 1 } { 4 }\)\(p\)\(3 p\)
    Two values of \(X\) are chosen at random. Determine the probability that their product is greater than their sum.
  2. A random variable \(Y\) takes \(n\) values, each of which is equally likely. Two values, \(Y _ { 1 }\) and \(Y _ { 2 }\), of \(Y\) are chosen at random. It is given that \(\mathrm { P } \left( Y _ { 1 } = Y _ { 2 } \right) = 0.02\).
    Find \(\mathrm { P } \left( Y _ { 1 } > Y _ { 2 } \right)\).