Rohit wants to check his IQ with an MCQ test. The test has five questions with one correct answer. Each question has three options. If he just randomly guesses the answer to each question, what is the probability that he will get exactly three questions correct?
0.165
To determine the probability that Rohit will get exactly three questions correct by random guessing, we use the binomial probability formula, since each question has a binary outcome (correct or incorrect). The probability for the binomial distribution is calculated as:
P(X = k) = C(n, k) * pk * (1-p)n-k
Where:
- n = total number of trials (questions) = 5
- k = number of successful trials (correct answers) = 3
- p = probability of success (correct answer) for each trial = 1/3, since there is one correct answer out of three options
We first calculate the binomial coefficient C(n, k) (combinations of choosing k successes in n trials), which is:
C(n, k) = n! / (k! * (n-k)!)
Calculating:
C(5, 3) = 5! / (3! * (5-3)!) = 10
Now we will calculate the probability:
P(X = 3) = C(5, 3) * (1/3)3 * (2/3)(5-3)
P(X = 3) = 10 * (1/27) * (4/9)
P(X = 3) = 10 * 1/27 * 4/9 = 40/243 ≈ 0.165
Therefore, the probability that Rohit will get exactly three questions correct is 0.165.
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