Is There a Methodical Way to Solve Complex Probability Problems?

[ScienceNewb]

So I have this probability question which I originally solved quite easily. What's frustrating is that I solved it in just a few neat steps, and then forgot how to do it. Now nobody can tell me how to solve it without trial and error.

A girl has a 0.7 chance of getting a goal for every shot she takes. Her coach wants her to keep shooting until the probability of getting 50 or more shots is 0.99... find the number of shots she needs to take.

The answer is 86

 

[vela]

What does 0.99... mean? If you mean an infinite number of 9s, that's equal to 1, so she'd have to take an infinite number of shots. You need to clear that up first.

Think about kind of distribution describes the probability of her making m shots out of n attempts.

 

[ScienceNewb]

What does 0.99... mean? If you mean an infinite number of 9s, that's equal to 1, so she'd have to take an infinite number of shots. You need to clear that up first.

Think about kind of distribution describes the probability of her making m shots out of n attempts.

The probability of getting 50 shots being greater than 0.99.

It's binomial distribution and the idea is to find the value of n. However the only method I can work out at this point is to make all the pr(X<50) to get the probability less than 0.01... if that makes sense. However this method would require about 50 calculations lol

If it helps I'm using a tnspire CAS calculator, and it's definitely a calculator question

 

[vela]

You can approximate the binomial distribution with a normal distribution with mean np and variance np(1-p).