Chapter 13.6, Problem 7CYU

To determine

Find the probability that at least one of them did not go to prom.

Answer to Problem 7CYU

About 17.2%

Explanation of Solution

Given:

In A’s senior class of 100 students , 91% went to the senior prom. Two people are chosen at random from the entire class .

Formula Used:

  $P(A\text{ and }B)=P(A)\cdot P(B)$ , where A and B are independent evens

  $P(\text{not }A)=1-P(A)$

Calculation:

We need to choose two people from the entire class and find the probability that atleast one of them did not go to prom.

The complementary of the given situation is , out of two , both went to the prom .

So, we find the probability that both people went to the prom , then we subtract it from the total probability to get the probability that at least one of them did not go to prom.

Probability that one person went to the prom is $\frac{91}{100}=0.91$

Both the events are independent .

So, $P(\text{both went to the prom)=}0.91\times 0.91=0.8281$

So, $P(\text{atleast one did not go to prom)=1}-0.8281=0.1719\approx 17.2\%$

So, the probability that atleast one out of randomly chosen two people did not go to prom is about 17.2%