Question

Casey ran out of time while taking a multiple-choice test and plans to guess on the last 101010 questions. Each question has 555 possible choices, one of which is correct. Let X=X=X, equals the number of answers Casey correctly guesses in the last 101010 questions.
Which of the following would find P(X=2)P(X=2)P, left parenthesis, X, equals, 2, right parenthesis?

Answer 1

Answer:

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is correct, or it is not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which  is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

There are four questions, so n = 4.

Each question has 5 options, one of which is correct. So  

What is the probability that he answers exactly 1 question correctly in the last 4 questions?

This is  

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Answer 2

Answer:

P(X=2)=

(10/2) (1/5)^2 (4/8)^8

Step-by-step explanation:

This has the correct binomial coefficient for 2 successes in 10 trials, the correct probabilities for success and failure, and the correct exponents for the number of successes and failures.