4 Clay pigeon shooting is the sport of shooting at special flying clay targets with a shotgun.
- Rhys, a novice, uses a single-barrelled shotgun. The probability that he hits a target is 0.45 , and may be assumed to be independent from target to target.
Determine the probability that, in a series of shots at 15 targets, he hits:
- at most 5 targets;
- more than 10 targets;
- exactly 6 targets;
- at least 5 but at most 10 targets.
- Sasha, an expert, uses a double-barrelled shotgun. She shoots at each target with the gun's first barrel and, only if she misses, does she then shoot at the target with the gun's second barrel.
The probability that she hits a target with a shot using her gun's first barrel is 0.85 . The conditional probability that she hits a target with a shot using her gun's second barrel, given that she has missed the target with a shot using her gun's first barrel, is 0.80 . Assume that Sasha's shooting is independent from target to target.
- Show that the probability that Sasha hits a target is 0.97 .
- Determine the probability that, in a series of shots at 50 targets, Sasha hits at least 48 targets.
- In a series of shots at 80 targets, calculate the mean number of times that Sasha shoots at targets with her gun's second barrel.
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