2026 HCI P2 Q6
2026 HCI P2 Q6
Junior College 2
8 marks
A game involves drawing two cards without replacement from a deck containing a total of 6 cards where three of the cards are marked '1', two of the cards are marked '2', and one of the cards is marked '3'. The score, \(X\), obtained is the sum of the two numbers of the two cards drawn.
- Show that \(\mathrm P(X=4)=\dfrac4{15}\).[2]
- Find the probability distribution of \(X\).[2]
- Find the values of \(\mathrm E(X)\) and \(\operatorname{Var}(X)\).[2]
- Given that now the game is repeated 100 times and the score for each round is recorded. Find the probability that the mean score of the 100 rounds is more than 3.4.[2]
Solution:
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Answer:(a) \(\frac4{15}\) (b) For \(x=2,3,4,5\), probabilities \(\frac15,\frac25,\frac4{15},\frac2{15}\), respectively. (c) \(\mathrm E(X)=\frac{10}3\), \(\operatorname{Var}(X)=\frac89\) (d) \(0.240\) (CLT approximation).
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