The probability of guessing any one is 1 out of 4, or 0.25.
Assume that the choices are made independently. Then, if X is the random variable which represents the number of successes (correct guesses), X is a Binomial variable with n = 5 and p = 0.25.
Then Prob(X = 3) = 5C3*p^3*(1-p)^(n-3)
= 10*(0.25)^3*(0.75)^2
= 0.088, approx.
64/256
Since there are 4 choices the probability of guessing any given answer correctly is 1/4 or .25; call this a success and denote it by p The chance of guessing wrong is .75; call this a failure and denote it by q. So the chance of 3 out of 5 correct answers is 5C3xp^3q^(5-3)=10p^3q^2 5C3x(.25)^3(.75)^2 5x4x3/3x2(.15625)(.5625) 10(.12625)(.5625)=.0877891
I regret that I do not have access to a study that looked at this matter and so do not have any experimental evidence.
The probability is 3/8 = 0.375
The probability is 90/216 = 5/12
64/256
It is 0.0033
The probability that she gets exactly 3 right is 8C3*(1/3)3*(2/3)5 = 0.2731 approx.
Since there are 4 choices the probability of guessing any given answer correctly is 1/4 or .25; call this a success and denote it by p The chance of guessing wrong is .75; call this a failure and denote it by q. So the chance of 3 out of 5 correct answers is 5C3xp^3q^(5-3)=10p^3q^2 5C3x(.25)^3(.75)^2 5x4x3/3x2(.15625)(.5625) 10(.12625)(.5625)=.0877891
I regret that I do not have access to a study that looked at this matter and so do not have any experimental evidence.
The probability is 2 - 6
The probability is 0.375
.125
P = (6!)/(6-4)!4!=15
The probability is 3/8 = 0.375
They are exactly the same
Exactly 1.