Question

To introduce her class to binomial distributions, Mrs. Desai gives a $10$-item, multiple choice quiz. The catch is, students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key, so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let $X=$the number of Patti's correct guesses.

Find $P(X=3)$. Explain what this result means.

Short answer

The value of$P(X=3)$is$0.2013$

Step-by-step solution

Given Information 

Number of questions$=10$

Students are supposed to guess the answers.

$X$is a number of answers that Patti gives correct.

Explanation

The binomial distribution pdf is:

$P(X=r)={}^{n}C_r\times p^r\times (1-p{)}^r$

Calculation:

Using Ti-83 plus calculator $P(X=3)$can be calculated as:

Thus, $0.213$is the required probability