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The objective of a game is to throw as many 6’es as possible with three dice...

The objective of a game is to throw as many 6’es as possible with three dice in two tries. The rules of the game are as follows:
Three fair dice are thrown once initially. If any 6’es turn up, the die or dice showing 6 are set aside. The remaining die or dice are thrown one more time. The total number of 6’es from the two throws is then noted.
Let ? be the random variable representing the number of 6’es after the two throws. Calculate the probability mass function of ?. Hence, calculate the expected value and variance of ?.

Math   Statistics-And-Probability   
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