Question

Question 3 (1 point)A retailer sends scratch-off coupons to registered customers; 30% of the coupons will reveal a discount of 50%.Before mailing, a manager selects 10 coupons at random from the stack of printed coupons and scratches toreveal the discount.What is the probability that exactly 1 of the coupons reveals a discount of 50%?Round to 3 decimal places.

Answer 1

Answer:

The probability that exactly 1 coupon reveals a discount of 50% is 0.121

Step-by-step explanation:

We want to find the probability X = 1.

Using the Binomial theorem, we have:

`\begin{gathered} P(X=k)=(\text{nCk)}p^k(1-p)^(n-k) \\ \\ p\text{ is the probability of success = 30\% = 0.3} \\ n\text{ is the sample size = 10} \\ k\text{ = 1} \end{gathered}`
`\begin{gathered} P(X=1)=(10C1)(0.3)^1(1-0.3)^(10-1) \\ \\ =10*0.3*0.7^9 \\ =0.121 \end{gathered}`