Sales

According to sales statistics, 77% of people buy item A and 58% buy item B. What is the probability that out of 15 people, exactly 8 buy item A and 7 buy item B?

Final Answer:

p =  1755.8 %

Step-by-step explanation:

$$\begin{gathered} p_1=77\%=\frac{77}{100}=0.77 \\ {p}_2=58\%=\frac{58}{100}=\frac{29}{50}=0.58 \\ {C}_8(15)=\left(\genfrac{}{}{0ex}{}{15}{8}\right)=\frac{15!}{8!(15-8)!}=\frac{15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}=6435 \\ P=\left(\genfrac{}{}{0ex}{}{15}{8}\right)\cdot p_1^8\cdot p_2^7=6435\cdot 0.77^8\cdot 0.58^7\doteq 17.5578 \\ p=100\cdot P=100\cdot 17.5578=1755.8\% \end{gathered}$$

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