Question

One hundred people were surveyed about their breakfast preferences. They had between french toast and pancakes and between sausage and bacon. The results the table below.

Category french toast pancakes

sausage 25 21

bacon 23 31

1. What is the probability that a randomly selected person from the survey prefers bacon.

2. What is the probability that a randomly selected person from the survey prefers pancakes?

3. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer bacon and pancakes?

4. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer sausage?

5. What is the probability that a randomly selected person from the survey prefers sausage given that they prefer french toast?

Answer 1

	French Toast	Pancakes	Total
Sausage	25	21	46
Bacon	23	31	54
Total	48	52	100

There are a total of 100 people.

Probability = Favourable Outcomes / Total Outcomes

1) P(Prefers Bacon) = 54/100 = 0.54

2) P(Prefers French Toast) = 48/100 = 0.48

3) P(Prefers Pancakes) = 52/100 = 0.52

4) By Bayes Theorem, P(A given B) = P(A/B) = P(A and B) / P(B)

Therefore P(Prefers toast given that they prefer sausage) = P(French Toast and Sausage) / P(Sausage) = (25/100) / (46/100) = 25/46 = 0.5345

5) P(Prefers sausage given that they prefer Toast) = P(French Toast and Sausage) / P(Toast) = (25/100) / (48/100) = 25/48 = 0.5208