A large bakery has many different products for sale. Suppose that 200 customers come in between 6 am and 10 am. Of the 200 customers, 140 order donuts, 100 order cinnamon rolls, and 80 order both. Suppose a customer is randomly selected. Find P(no donuts and no cinnamon rolls).

Answers

Answer 1

Out of 200 customers, the probability of a customer not ordering either donuts or cinnamon rolls is 0.2 or 20%.

Use the concept of probability defined as:

For the occurrence of an event, it is a ratio of the number of favorable outcomes to the number of total outcomes.

Given that,

Time frame: 6 am to 10 am

Total number of customers: 200

Number of customers who ordered donuts: 140

Number of customers who ordered cinnamon rolls: 100

Number of customers who ordered both donuts and cinnamon rolls: 80

To find the probability of a customer ordering neither donuts nor cinnamon rolls:

Subtract the probability of a customer ordering either donuts or cinnamon rolls or both from 1.

Now calculate:

Probability of ordering donuts:

140 out of 200 customers ordered donuts,

The probability of ordering donuts is,

140/200 = 0.7.

Probability of ordering cinnamon rolls:

100 out of 200 customers ordered cinnamon rolls,

The probability of ordering cinnamon rolls is,

100/200 = 0.5.

Probability of ordering both donuts and cinnamon rolls:

80 out of 200 customers ordered both,

The probability of ordering both is,

80/200 = 0.4.

Now, to find the probability of a customer ordering neither donuts nor cinnamon rolls,

Subtract the probability of ordering either or both from 1:

P(no donuts & no cinnamon rolls) = [tex]1 - P( \text{donuts}) - P(\text{cinnamon rolls}) + P(\text{donuts & cinnamon rolls})[/tex]

[tex]\text{P(no donuts & no cinnamon rolls)}= 1 - 0.7 - 0.5 + 0.4[/tex]

[tex]\text{P(no donuts & no cinnamon rolls)} = 0.2[/tex]

Hence,

The probability of a customer not ordering either donuts or cinnamon rolls is 0.2 or 20%.

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