2020 HCI P2 Q8
A set of $9$ cards are numbered $1$, $1$, $2$,$3$, $3$, $4$, $5$, $5$ and $6$. A round of matching game is played where two cards are drawn, one at a time without replacement. A match occurs when the two cards drawn have the same number.
(i)
Given that the sum of the numbers on the two cards is less than $5$, find the probability of a match occurring in a game. Hence, or otherwise, determine if having a match is independent of having a sum of the numbers on the cards less than $5$ for a game.
[3]
(ii)
Dave decides to try his luck at this game repeatedly until he obtains a match. What is the least number of rounds he will have to attempt such that the probability of obtaining a match is at least $75\%$?
[4]
(iii)
Instead of drawing only two cards in a round, Dave continues to draw the cards until he obtains a match. He draws one card at a time without replacement. Find the probability that a match occurs on his third draw.
[2]
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