2018 SRJC P2 Q7

A player throws an unbiased six-sided die and the number shown on the top face is noted.If it is not a six, the score is the number shown on the top face.If it is a six, he throws the die a second time and the score is the total score obtained from his two throws.The player has at most two throws.

1. Construct the probability distribution table on the score for the player.[2]

Given that the expected player’s score is \(\frac{49}{12}\),

2. find the exact value of the variance of the player’s score, showing your workings clearly.[3]