Question

The probability that a student gets admission to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 2 are accepted?

Answer 1

1

Answer on Question #74855, Math / Statistics and Probability

Q. The probability that a student gets admission to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 2 are accepted?

Solution:

To determine the probability of at most 2 students out of 5 will get accepted in college, there is need to compute 3 individual probabilities by applying the following binomial formula:

$$P(x) = \frac{n!}{x! (n - x)!} P^x q^{n - x}$$

Where,

$$n = 5$$

P (probability of success) = 0.3

$$q = 1 - P$$

The calculation of probability is as follows:

$$\begin{array}{l} b(\times \leq 2; 5, 0.3) = b(\times = 0; 5, 0.3) + b(\times = 1; 5, 0.3) + b(\times = 2; 5, 0.3) \\ = \left[ \frac{5!}{5! (5 - 0)!} (0.3)^0 (1 - 0.3)^{5 - 0} \right] + \left[ \frac{5!}{5! (5 - 1)!} (0.3)^1 (1 - 0.3)^{5 - 1} \right] \\ + \left[ \frac{5!}{5! (5 - 2)!} (0.3)^2 (1 - 0.3)^{5 - 2} \right] \\ = 0.1681 + 0.3601 + 0.3087 \\ \Rightarrow 0.8369 \\ \end{array}$$

As per this, there is $83.69\%$ probability that at most 2 students get accepted out of 5 applications.

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