Suppose that past history show that 60% of students prefer Brand C cola. A sample of 5 students is selected. What is the probability that at most 2 of the 5 students selected will prefer Brand C?

Answer:

Given:

Probability of success $(p)=0.6$

Sample size $(n) = 5 $

Solution:

The probability that at most 2 of the 5 students selected will prefer brand C:

$$P(x \leq 2) = \sum_{0}^{2} \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} $$ $$= \sum_{0}^{2} \binom{5}{x} \cdot 0.6^x \cdot (1 – 0.6)^{5 – x} $$ $$= 0.3174$$

Final Answer:

The probability that at most 2 of the 5 students selected will prefer brand C $=0.3174$