Question

The probability that two students give the same wrong answer on a 4 answer multiple choice question, assuming that they're answering completely at random, is 1/3. What's the probability that, out of 10 wrong answers, at least 7 of them are the same wrong answer? A. 0.9803 B. 0.0197 C. 0.9966 D. 0.0034

Answer 1

Solution:

Let us given that n = 10, and p = 1/3 so now we need to find the probability that P(X>=7)

Now by using rules of probabilities P(X>=7)

Now by using Binomial distribution formula P(X=x) = nCx p^x (1-p)^(n-x)

Here P(X>=6) = P(X=7) + P(X=8) + P(X=9) + P(X=10)

now just plug the values in the formula and get the answer,

P(X>=6) = 10C7 * (1/3)^7 (1- 1/3)^3 + ... + 10C10 * (1/3)^10 (1- 1/3)^0 = 0.0197

Hence option B = 0.0197 is correct option.

Best Luck !