3 A spinner has 5 sides, numbered 1, 2, 3, 4 and 5 . When the spinner is spun, the score is the number of the side on which it lands. The score is denoted by the random variable \(X\), which has the probability distribution shown in the table.
| \(x\) | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( X = x )\) | 0.3 | 0.15 | \(3 p\) | \(2 p\) | 0.05 |
- Find the value of \(p\).
A second spinner has 3 sides, numbered 1, 2 and 3. The score when this spinner is spun is denoted by the random variable \(Y\). It is given that \(\mathrm { P } ( Y = 1 ) = 0.3 , \mathrm { P } ( Y = 2 ) = 0.5\) and \(\mathrm { P } ( Y = 3 ) = 0.2\).
- Find the probability that, when both spinners are spun together,
(a) the sum of the scores is 4,
(b) the product of the scores is less than 8 .