Originally Posted by **toranc3** Nice and thanks! Could you help me with part b? I am not sure how to do it. Just give me a few hints.
Here is part b
If there are 1000 pellets, and they fall in a uniform distribution over a circle with the radius calculated in part a, what is the probability that atleast one pellet will fall on the head of a person who fires the shotgun? Assume that his head has a radius of 0.1m.
I know how to do probabilty with a quarter but not this ha. Also what does it mean when they say uniform distribution? |

The first hint is a good one to remember when doing probability of "

**at least** one." Rather than calculate P(1) + P(2) + ..., it is "always" easier to calculate P(0) and subtract that from unity:

P(at least 1) = 1 - P(none)

Remembering that rule will save you a lot of work some day. Turns out it won't make any difference this time, but some day...

Another law of probabilities you have to use us that the probability of a number of

**independent events** is the

**product **of the probabilities of the individual events. So if you determine the probability q that one pellet misses the head, then you can raise that probability to the power 1000 to get P(none).

P(at least 1) = 1 - P(none) = 1 - q^1000

A

**uniform distribution** means that the probability is equal anyplace within the the boundary. If a pellet falls at random within a circle or radius 80 m, what is the probability p that it falls withing a circle of radius 0.1m? Probability of a miss is q=1-p, and you can go from there.

-OR-

Since p is so small, you could get away with the approximation that

P(at least 1) ~ P(1) ~ 1000×p

That is close enough!