4 A game for two players is played using a fair 4-sided dice with sides numbered 1, 2, 3 and 4. One turn consists of throwing the dice repeatedly up to a maximum of three times. When a 4 is obtained, no further throws are made during that turn. A player who obtains a 4 in their turn scores 1 point.
- Show that the probability that a player obtains a 4 in one turn is \(\frac { 37 } { 64 }\).
Xeno and Yao play this game. - Find the probability that neither Xeno nor Yao score any points in their first two turns.
- Xeno and Yao each have three turns.
Find the probability that Xeno scores 2 more points than Yao.
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