May/June 2026 Paper 52

Ling has three coins. Each coin is biased so that the probability of obtaining a head is $\frac{1}{3}$. Ling throws all three coins at the same time. The random variable $X$ denotes the number of heads that Ling obtains. Draw up the probability distribution table for $X$.

Ling throws all three coins at the same time repeatedly. Find the probability that he obtains at least two heads for the first time on his 7th throw.

Find the probability that he obtains at least two heads for the second time on his 6th or 7th throw.