Question

Lunch at school consists of a sandwich, a vegetable, and a fruit. Each lunch combination is equally likely to be given to a student. The students do not know what lunch they will get. Sol's favorite lunch is a chicken sandwich, carrots, and a banana.
a. Make a tree t agram to determine how many different lunches are possible,
b. What is the probability that Sol gets his favorite lunch le. List all the possible outcomes ? Explain your reasoning
c. What is the lunch items? Explain probability that Sol gets at least one of his favorite

Answer 1

Answer:

a) see attachment

b) Pr(chicken sandwich, carrots, and a banana) = 1/12

c) The probability that Sol gets at least one of his favorite = 5/6

Step-by-step explanation:

a) A tree diagram is used to represent sample space.

We are told the lunch choices are sandwich, a vegetable and a fruit and each lunch combination are possible.

Find attached the tree diagram.

From the tree diagram, there are a total of 12 possible outcomes.

b) Sol's favorite lunch is a chicken sandwich, carrots, and a banana.

The probability that Sol gets his favorite lunch = Pr(chicken sandwich, carrots and a banana)

Pr(chicken sandwich, carrots, and a banana) = 1/12

Reason: From the tree diagram, the likelihood of having all three (chicken sandwich, carrots and a banana) occurs only once.

Pr(chicken sandwich, carrots and a banana) = [number of times(chicken sandwich, carrots and a banana) occurs]/(total number of possible outcomes)

Pr(chicken sandwich, carrots, and a banana) = 1/12

c) For Sol to get at least one of his favorite, we would have at least either chicken, carrot or banana in the possible outcome.

We have 10 of such possible outcome:

Chicken, carrot and apple

Chicken, carrot and banana

Chicken, spinach and apple

Chicken, spinach and banana

Hamburger, carrot and apple

Hamburger, carrot and banana

Hamburger, spinach and banana

Turkey, carrot and apple

Turkey, carrot and banana

Turkey, spinach and banana

The probability that Sol gets at least one of his favorite = (total number of at least one of Sol's favorite lunch)/(total possible outcome)

= 10/12 = 5/6

The probability that Sol gets at least one of his favorite = 5/6