Answer & Explanation
In a fair die, there are 6 possible outcomes, 1, 2, ..., 6, all of which are equally likely, that is, with probability
On rolling the fair die once, the probability of getting 1 or 2 is
Similarly, the probability of getting 3 or 4 is 1/3, and the probability of getting 5 or 6 is 1/3.
Thus, in case of each of the 11 questions, the probability of selecting each option is 1/3.
As the outcomes on the roll of a fair die are independent from one roll to another, the choices made in the different questions are also independent of one another.
Considering each attempted question as a trial, there are
Considering it to be a success if the correct option is chosen, the probability of success in each trial is
Here, X can be considered as the number of successes, that is, number of questions correctly answered. Thus, X has a binomial distribution with parameters,
Since p denotes the probability of success, the probability of failure is,
The probability mass function of X here is:
The probability of exactly 4 correct answers, that is, exactly 4 successes is calculated below:
Thus, the probability of exactly 4 correct answers is 0.238446.
Binomial Problem with
Find the probability of
a) exactly four correct answers
b) fewer than three correct answers
Hence, the probability of getting the correct answer is
Note that the probability of x successes out of n trials is
Thus, the probability is
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