SPS SPS SM Statistics 2025 April — Question 7

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2025
SessionApril
TopicDiscrete Probability Distributions
TypeVerify probability from combinatorial selection
7. Miguel has six numbered tiles, labelled \(2,2,3,3,4,4\). He selects two tiles at random, without replacement. The variable \(M\) denotes the sum of the numbers on the two tiles.
  1. Show that \(P ( M = 6 ) = \frac { 1 } { 3 }\) The table shows the probability distribution of \(M\)
    \(m\)45678
    \(P ( M = m )\)\(\frac { 1 } { 15 }\)\(\frac { 4 } { 15 }\)\(\frac { 1 } { 3 }\)\(\frac { 4 } { 15 }\)\(\frac { 1 } { 15 }\)
    Miguel returns the two tiles to the collection. Now Sofia selects two tiles at random from the six tiles, without replacement. The variable \(S\) denotes the sum of the numbers on the two tiles that Sofia selects.
  2. Find \(P ( M = S )\)
  3. Find \(P ( S = 7 \mid M = S )\)
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