- In a game, a player can score \(0,1,2,3\) or 4 points each time the game is played.
The random variable \(S\), representing the player's score, has the following probability distribution where \(a , b\) and \(c\) are constants.
| \(s\) | 0 | 1 | 2 | 3 | 4 |
| \(\mathrm { P } ( S = s )\) | \(a\) | \(b\) | \(c\) | 0.1 | 0.15 |
The probability of scoring less than 2 points is twice the probability of scoring at least 2 points.
Each game played is independent of previous games played.
John plays the game twice and adds the two scores together to get a total.
Calculate the probability that the total is 6 points.