91Ó°ÊÓ

Given in the question that, according to the Mars candy company, $20\%$of its plain M&M’s candies are orange. Assume that the company’s claim is true. Suppose that you reach into a large bag of plain M&M’s (without looking) and pull out $8$candies. Let$X$ = the number of orange candies you get.

Given:

Probability of success $\left(p\right)=20\%=0.20$.

Number of trials $\left(n\right)=8$

Calculation:

Here, $\mathrm{X}$is a random variable that indicates the number of orange candies.

The probability of selecting $0$orange candies is:

$P(X=0){=}^8{C}_0×(0.20{)}^0×(1−0.20{)}^{8−0}$

$=0.1678$

Thus, the probability is$0.1678.$

Here, probability is above$5\%$. Thus, the event is not surprising.

Given in the question that, According to the Mars candy company, $20\%$ of its plain M&M’s candies are orange. Assume that the company’s claim is true. Suppose that you reach into a large bag of plain M&M’s (without looking) and pull out 8 candies. Let $X$ = the number of orange candies you get.

The probability of selecting more than $5$orange candies is calculated as:

$P(Xâ‰\yen 5)=1−P(X<5)$

$=1−\left[P\right(X=0)+P(X=1)+….+P(X=4\left)\right]$

$=0.0104$

Thus, the probability is $0.0104$.

Here, probability is below $5\%$. Thus, the event is surprising to happen.