N2014 P2 Q7

Yan has a fair six-sided die and a biased six-sided die. The faces on each die are numbered \(1\), \(2\), \(3\), \(4\), \(5\) and \(6\).

1. Yan throws the fair die \(10\) times. Find the probability that he obtains exactly three \(6\)s.[1]
2. Yan throws the fair die \(60\) times. Use a suitable approximation to find the probability that he obtains between \(5\) and \(8\) \(6\)s inclusive.[3]

The probability of obtaining a \(6\) on the biased die is \(\frac1{15}\).

3. Yan throws the biased die \(60\) times. Use a suitable approximation to find the probability that he obtains between \(5\) and \(8\) \(6\)s inclusive.[3]