Math Help - Simple probability or more advanced technique?

1. Simple probability or more advanced technique?

Hi everyone, I have two questions regarding a homework question (set out below):

1. Can this question be addressed using simple probability or is a more advanced probability technique required (e.g. using a probability distribution)?
2. What does “include the endpoints” mean? (This term is confusing me because I don't think it is normally used in simple probability calculations).

Homework question:
15%of car crashes result in severe injury to at least one person involved in thecrash. If there are 25 major car crashes per month, calculate the followingprobabilities:

in 25 major crashes, exactly five result in severe injury

in 25 major crashes, between two and eight result in seriousinjury? (include the endpoints)

in 25 major crashes, no severe injuries occur

in 25 major crashes, at least one severe injury occurs

2. Re: Simple probability or more advanced technique?

I teach the binomial distribution to final year high school students here in Oz. They seem to understand it.

Your problem is binomial with p=0.15 and n=25. Let X be the occurrance of a serious injury.

Note $P(X=k) = \binom{n}{k}p^k\times (1-p)^{n-k}$

For the first question find P(X=5)

For the second find P(X=2)+P(X=3)+...+P(X=8)

For the third find P(X=0)

For the forth P(X>0) = P(X=1)+P(X=2)+...+P(X=25) or even easier 1-P(X=0)

Does this help?

3. Re: Simple probability or more advanced technique?

Originally Posted by pickslides

I teach the binomial distribution to final year high school students here in Oz. They seem to understand it.

Your problem is binomial with p=0.15 and n=25. Let X be the occurrance of a serious injury.

Note $P(X=k) = \binom{n}{k}p^k\times (1-p)^{n-k}$

For the first question find P(X=5)

For the second find P(X=2)+P(X=3)+...+P(X=8)

For the third find P(X=0)

For the forth P(X>0) = P(X=1)+P(X=2)+...+P(X=25) or even easier 1-P(X=0)

Does this help?
Thanks so much - this has been very helpful.