Resolved: "A Finite final consists of 50 multiple choice..."

glamrockqueen7

Answered question

2021-09-24

A Finite final consists of 50 multiple choice questions. If each question has 5 choices and 1 right answer, find the probability that a student gets an A (i.e. 45 or better) by purely guessing on each question.

Answer & Explanation

crocolylec

Skilled2021-09-25Added 100 answers

Step 1
The Binomial probability distribution is:
$P (X = x) = (\begin{matrix} n \\ x \end{matrix}) (p)^{x} (1 - p)^{n - x}$
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
The random variable X is defined as the number of correct answers which follows binomial distribution with probability of success $0.20 (= \frac{1}{5})$ and sample size 50.
Step 2
The probability that a student gets an A (i.e. 45 or better) is,
$P (X \geq 45) = P (X = 45) + P (X = 46) + \dots + P (X = 50)$
$= (\begin{matrix} 50 \\ 45 \end{matrix}) (0.20)^{45} (1 - 0.20)^{50 - 45} + (\begin{matrix} 50 \\ 46 \end{matrix}) (0.20)^{46} (1 - 0.20)^{50 - 46} + \dots + (\begin{matrix} 50 \\ 50 \end{matrix}) (0.20)^{50} + (1 - 0.20)^{50 - 50}$
$= 0 + 0 + 0 + 0 + 0 + 0$
$= 0$
Thus, the probability that a student gets an A (i.e. 45 or better) is 0.

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