Question

tree diagram probability

1. you go to the snack bar to buy a bagel and a drink for lunch. you can choose from a plain bagel, a blueberry bagel, or a raisin bagel. the choices for a drink include water or a sports drink. how many different lunches could you make with these choices? what is the probability of getting a blueberry bagel and a sports drink?

plain bagel
water
sports drink
blueberry bagel
water
sports drink
raisin bagel
water
sports drink
6 different lunches
3 x 2 = 6
blueberry bagel
and sports drink
⅓ · ½ = 1/6

1. when you get dressed for school you open your closet to find that you have the following choices: a red, blue, or white shirt; jeans or sweatpants; tennis shoes or sandals. how many different outfits could be made with these choices? what is the probability of wearing a white shirt, sweatpants and sandals?

3×2×2=12
red
s
sandals
j
blue
s
j
white
s
j

Explanation:

Problem 1:

Step1: Calculate total lunches

We have 3 bagel choices and 2 drink choices. Using the multiplication principle (total combinations = number of bagel choices × number of drink choices), we get \( 3\times2 = 6 \).

Step2: Calculate probability

The probability of choosing a blueberry bagel is \( \frac{1}{3} \) (since there are 3 bagels) and the probability of choosing a sports drink is \( \frac{1}{2} \) (since there are 2 drinks). For independent events, we multiply the probabilities: \( \frac{1}{3}\times\frac{1}{2}=\frac{1}{6} \).

Step1: Calculate total outfits

We have 3 shirt choices, 2 pants choices, and 2 shoe choices. Using the multiplication principle (total combinations = number of shirt choices × number of pants choices × number of shoe choices), we get \( 3\times2\times2 = 12 \).

Step2: Calculate probability

The probability of choosing a white shirt is \( \frac{1}{3} \), sweatpants is \( \frac{1}{2} \), and sandals is \( \frac{1}{2} \). For independent events, we multiply the probabilities: \( \frac{1}{3}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{12} \).

Answer:

• Number of different lunches: \( 6 \)
• Probability of blueberry bagel and sports drink: \( \frac{1}{6} \)

Problem 2: