Probability Question:
A college student claims that she can identify 3 different types of cheese by taste. An experiment is set up to test her ability. She is blindfolded and given three pieces of cheeses, each representing a different brand. What is the probability that she will correctly identify TWO out of the three pieces of cheese ?
a; 0.11
b:0.16
c:0.33
d:0.67
ive worked it out using a binomial probability distribution equation and the answer works out to 0.22 which is not an option on the multiples choice question.
If possible please give an explanation or show working out for understanding.
Any assistance will be appreciated.
Thank You
This is my interpretation of the question:
R-- right
W -- wrong
there are 8 ways for the selection to take place
(or there are 2 ways to pick the first cheese, right or wrong, 2 ways to pick the 2nd, and 2 ways to pick the third:
2x2x2=8 )
WWW
WWR **
WRW **
WRR
RWW **
RWR
RRW
RRR
Of these there are 3 choices in which exactly 2 are right
so the prob of picking 2 right = 3/8 = .375
(none of the choices)
It has to be one of the choices Reiny. its an multiple choice you have to circle.
To find the probability that the college student will correctly identify two out of the three pieces of cheese, we can use the binomial probability formula. In this case, each cheese has a 1/3 chance of being identified correctly.
The formula for the binomial probability is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- n is the number of trials (in this case, 3 because there are 3 pieces of cheese)
- k is the number of successes (in this case, 2 because the student needs to correctly identify 2 out of 3)
- p is the probability of success in a single trial (1/3, since there are 3 types of cheese)
Using this formula, we can calculate the probability as follows:
P(X=2) = (3 choose 2) * (1/3)^2 * (1 - 1/3)^(3-2)
= 3 * (1/9) * (2/3)
= 6/27
≈ 0.22
As you correctly calculated, the probability is approximately 0.22. It seems that none of the options provided in the multiple-choice question match this result. It could be a mistake in the options or a rounding error.
Therefore, none of the options provided are the correct probability, and the correct answer would not be available in the multiple-choice question you have.