00:01
For this problem, we have a multiple choice exam with six questions.
00:05
Each question has four multiple choice answers, a, b, c, and d, and the person writing the exam has not studied and decides to randomly guess at the answers.
00:17
So therefore, we can say out of the six questions, for each of them, the probability of guessing correctly is 1 out of 4, or 0 .25.
00:28
Now let's define x as the number of questions that are guessed correctly.
00:31
Here, x is a binomial random variable, and the binomial random variable has two parameters, the probability of success, and the number of trials.
01:03
Also for a binomial random variable, the probability mass function is given by this formula.
01:22
So for part a, we want the probability that one question is guessed right, so that is the probability that x equals 1.
01:31
In this case, the probability mass function simplifies to 0 .5 to the exponent 1.
01:42
Actually, that's 6 choose 1 times 0 .25 to the exponent 1 times 0 .75 to the exponent 5.
01:56
And this comes out to a probability of 0 .3560.
02:03
For b, we are asked for the probability that all questions are guessed correctly.
02:07
That's the probability that x equals 6.
02:15
And this is 0 .25 to the exponent 6...