Question

Wilma bought 4 boxes of Crunch-a-lot cereal. One out of every 5 boxes has a coupon for a free box of Crunch-a-Lot. What is the probability that Wilma got 2 coupons?

Answer 1

We have been given that Wilma bought 4 boxes of Crunch-a-lot cereal.

Further, we know that one out of every 5 boxes has a coupon for a free box of Crunch-a-Lot. We need to figure out the probability that Wilma got 2 coupons?

This question is based on Bernoulli's Trials. We know that probability for r successful draws out of n trials is given by:

$_{r}^{n}\textrm{C}(p)^{r}(1-p)^{n-r}$

We have $p=\frac{1}{5},n=4,r=2$. Upon substituting these values in this formula, we get:

$_{2}^{4}\textrm{C}(\frac{1}{5})^{2}(1-\frac{1}{5})^{4-2}\\ \\ 6\times (\frac{1}{5})^{2}(\frac{4}{5})^{2}\\ \\ 6\times \frac{1}{25}\times \frac{16}{25}\\ \\ \frac{96}{625}\approx 0.1536$

This is the required probability.