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Convert the hit count into a score

Teams of 8 people enter a shooting competition. Each member of a team takes a shot at the target. The number of points scored by a team is obtained by 2x2x where xx is the number of shots that hit the target. For a particular team, each member of the team independently has a probability of 0.75 of hitting the target.

(i) Find the probability that a randomly chosen team scores more than 6 points.

(ii) Find the number of points that a team is most likely to score.

CJC · Discussion · Question 7

Translate the score condition into a condition on the hit count before using the distribution.

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