Question

Hi I'm having problems solving probability. Can someone please help me? It is driving me crazy.

Answer 1

sure whats the question

Answer 2

in can try.

Answer 3

K, thank u. One second...

Answer 4

Ok, the question is: "What is the probability of answering at least 1 question out of 5 correctly?"

Answer 5

..."Each question has 4 possible choices"

Answer 6

1/5

Answer 7

I added what I thought were the probability of getting exactly 1, exactly 2 ... and so on to 5 up. But I did not get the right answer : (

Answer 8

This is how I set it up:
(.25*.75^4)+(.25^2*.75^3)+(.25^3*.75^2)+(.25^4*.75)+(.25^5)=

Answer 9

well its 1-prob of 0 out of 5 correctly
since there are 4 choices, the probability of choosing the correct choice is 1/4
probability of choosing wrong answer is 3/4
probability of getting all questions wrong is (3/4)^5
So the answer is 1 - (3/4)^5

Answer 10

1/4 = .25 = probability of getting an answer correct
3/4 = .75 = probability of getting an answer incorrect

Answer 11

*reading your answer now...

Answer 12

Try to find the probability of answering all the questions incorrectly, and lets call that P. The probability of answering at least one question correctly 1 - P, since it's the probability of not answering all questions incorrectly.
The probability of answering one question incorrectly is:
\[\frac{3}{4},\]since three out of four choices are wrong. Because there are five questions, you have to multiply this number by itself five times, so\[P = \left(\frac{3}{4}\right)^5\]and the probability of answering at least one question correctly is\[1-P = 1-\left(\frac{3}{4}\right)^5 = \frac{781}{1024} = 0.762695.\]

Answer 13

ok, i think I understand. so does that mean that the probability of getting at lest 2 correct = 1 - (3/4)^5 ?

Answer 14

Also, is it always a good idea to do "at least" problems as "1 - probability of the opposite"?

Answer 15

math_moron, you actually almost had it set up correctly
you just forgot the coefficients, 5Cx where x is the number of correct questions

Answer 16

5(.25*.75^4)+10(.25^2*.75^3)+10(.25^3*.75^2)+5(.25^4*.75)+(.25^5)

Answer 17

Sorry I'm just trying to wrap my head around what you did there

Answer 18

No, the probability of getting at least one correct is\[1-\left(\frac{3}{4}\right)^5.\]The probability of getting at least two correct is\[P=1-\left(\frac{3}{4}\right)^5 - Q\]where Q is the probability of getting exactly one correct, which is\[Q = \binom{5}{1}\frac{1}{4}\left(\frac{3}{4}\right)^4\]that is, the probability of answering one correctly (1/4) times the probability of answering the other four incorrectly ((3/4)^4) times five which is the number of ways of choosing one question out of five, so\[P = 1 - \left(\frac{3}{4}\right)^5-5\frac{1}{4}\left(\frac{3}{4}\right)^4 = \frac{47}{128} = 0.3671875.\]

Answer 19

ok, I think I'm starting to see it. Thank u all!
I'm unfamiliar w/ how this site works as this is my first time. Is there a way for me to award you points for helping me?

Also, is anyone aware of additional resources I can use for this topic?

Answer 20

Click on the good answer button next to our answer. You can look up "binomial probability" for more information.

Answer 21

Ok thank u for your help. I will look that up after I find this "good answer button" : )