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:

$$P(x\le 2)=\sum _0^2(\genfrac{}{}{0ex}{}{n}{x})\cdot p^x\cdot (1–p{)}^{n–x}$$ $$=\sum _0^2(\genfrac{}{}{0ex}{}{5}{x})\cdot {0.6}^x\cdot (1–0.6{)}^{5–x}$$ $$=0.3174$$

Final Answer:

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