Question

3

2
3
4
5
6
7
5
0.16
1 point
The contingency table below represents the percentage of customers at a local gas station who bought gas (G) or an automated car
wash (W).
BUY
GAS?
CAR
WASH?
YW NW
YG .22 .56
NG
.06 .16
TOTAL 28
.72
TOTAL
.78
.22
1.00
Calculate the probability...
Someone buys gas OR does not buy a car wash. P(YG U NW) =
(decimal form rounded to 3 places)
DO

Answer 1

The probability that someone buys gas OR does not buy a car wash, P(YG U NW), is calculated using the principle of inclusion-exclusion and the values from the contingency table, resulting in 0.940.

Step-by-step explanation:

To calculate the probability that someone buys gas OR does not buy a car wash, denoted as P(YG U NW), we use the contingency table provided. According to the principle of inclusion-exclusion in probability, the probability of the union of two events, A and B, is given by P(A U B) = P(A) + P(B) - P(A and B).

In this scenario, event A is 'buys gas' (YG) and event B is 'does not buy a car wash' (NW). The probabilities from the contingency table are P(YG) = 0.22 + 0.56 = 0.78, P(NW) = 0.56 + 0.16 = 0.72, and P(YG and NW) = 0.56. So, P(YG U NW) = P(YG) + P(NW) - P(YG and NW) = 0.78 + 0.72 - 0.56 = 0.94.

Therefore, the probability that someone buys gas OR does not buy a car wash is 0.940, rounded to three decimal places as requested.