1. ## Binomial Distribution Problem

Use the binomial formula to calculate the probability that a given baseball team will win more than one game out of a total of ten. Show the appropriate formula.

Hey guys, I forgot what I'm supposed to do here.

2. If $p$ is the probability of the team winning any given game then the probability of that team winning more than one game in ten is:
$1-(1-p)^{10}-10p(1-p)^9.$

Now can you explain why?

3. No, I can't because I hate probability. I'm a math tutor at a college and a student has this question and we're short staffed, and AAAAAaaargh.

But, long story short, no. But I would like to know why.

4. That is the opposite of winning none or exactly one.

5. You're awesome Plato. So, $(1-p)^{10}+10p(1-p)^9$ represents what quantity again?

6. Originally Posted by VonNemo19
You're awesome Plato. So, $(1-p)^{10}+10p(1-p)^9$ represents what quantity again?
Won't that be the probability of them winning one or no games? Or in other words, losing 10 or 9 games.

7. Hello, janvdl!

Plato is absolutely correct!

Won't that be the probability of them winning one or no games?
Or in other words, losing 10 or 9 games? . Yes!

Read the question again: "... more than one game ..."

This means: .2, 3, 4, ... or 10 wins.

The opposite is indeed: .0 or 1 win.

8. $P(X=2)+P(X=3)+P(X=4)+\dots +P(X=10) = 1 - (P(X=0)+P(X=1))$