There's 5 multiple choice questions on a quiz. Four choices to each question. Find the probability that the student gets 3 or more questions right.
p(x=3) (.25)^3= 0.015
p(x=4) (.25)^4=3.906
p(x=5) (.25)^5=9.765
Do you add them all together to get the overall probability?
First off, no probability can be more than 1, so you calculations are off.
P(x=3) = 5C3 .25^3 .75^2
P(x=4) = 5C4 .25^4 .75^1
P(x=5) = 5C5 .25^5 .75^0
Having gotten those, yes, you add them up.
I calculated them on my calculator so I borrowed my friends (since mine was messing up).
I got
P(x=3) = 5C3 .25^3 .75^2 = 0.008
P(x=4) = 5C4 .25^4 .75^1 = 0.003
P(x=5) = 5C5 .25^5 .75^0 = 0.0007
added up =0.01.
Did I calculate correctly
Hmmm. I got .08789 + .01465 + .00097 = .10352
Looks like you have some problems. Make sure you are calculating your binomial coefficients correctly.
Where did you get the .25 and .75 from?
To find the probability that the student gets 3 or more questions right, you need to add the probabilities of each individual case: p(x=3), p(x=4), and p(x=5). Adding them together gives you the overall probability.
So, in this case, you would calculate:
Overall probability = p(x=3) + p(x=4) + p(x=5)
Plugging in the values you've already calculated:
Overall probability = 0.015 + 3.906 + 9.765
Therefore, the overall probability that the student will get 3 or more questions right on the quiz is 13.686.