probability / combined fractions question (real-life) pls help!!!?

Question

I'm applying to 4 different schools.

For the first one I have approximately a 50% chance of getting into it ( or 2/4 in terms of fractions)

For the other 3, I have about a 25% chance of getting into them (or 1/4 in terms of fractions)

Can anyone explain how to figure out the odds that I'll get into AT LEAST ONE of these schools ????

THANKS SO MUCH!

Answer 1

Well we just started probablity in my Stats class, so you have to subtract the probablity you won't get into any of them from 1, the sum of all the probabilities.

P(you won't get into any) = P(not getting into the 1st) * P(not getting into the 2nd) * P(not getting into the 3rd) * P(not getting into the 4th)
P(you won't get into any) = .5 * .75 * .75 * .75
P(you won't get into any) = .211

1 - .211 = .789

So you have approximately 78.9% of getting into AT LEAST ONE of the schools. Those are good odds, I think.

Good luck!

Answer 2

If this is just a math problem, the standard assumption is that the probability of getting into one school is independent of getting into the others. In that case, take one minus the probability of not getting into any schools.

1 - P(0) = 1 - (1/2)*(3/4)^3 = 1 - 27/128 = 101/128
= .7890625

Since you mentioned real life, the probabilities won't be independent. If one school likes you, the probability that another school will like you increases, and conversely.

Answer 3

well you find the odds that you won't get in anywhere and then do 1-that

So .5*27/64=27/128 therefore the answer is 1-27/128 which is 101/128 which is approx. 79% chance that you will get in SOMEWHERE