6 Harry has three coins:
- One coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 3 }\).
- The second coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 4 }\).
- The third coin is biased so that the probability of obtaining a head when it is thrown is \(\frac { 1 } { 5 }\).
Harry throws the three coins. The random variable \(X\) is the number of heads that he obtains.
- Draw up the probability distribution table for \(X\).
Harry has two other coins, each of which is biased so that the probability of obtaining a head when it is thrown is \(p\). He throws all five coins at the same time. The random variable \(Y\) is the number of heads that he obtains. - Given that \(\mathrm { P } ( Y = 0 ) = 6 \mathrm { P } ( Y = 5 )\), find the value of \(p\).