Geometry - Conditional Probability Intro

Joyce rolls a dice. What is the probability that she rolled a 2 given that she rolled an even number? Please type your answer as a fraction in its simplest form with no spaces and a slash in between (eg. "5/6").

(a)  

André rolls a dice. What is the probability that he rolled a 2 if we know he did not roll a 5? Please type your answer as a fraction in its simplest form with no spaces and a slash in between (eg. "5/6").

(a)  

Phoebe is playing Big 2 (no joker, just the regular 52 cards) with her friends. What is the probability that the first card she gets is an ace? Please type your answer as a fraction in its simplest form with no spaces and a slash in between (eg. "5/6").

(a)  

(Statistics for this question are made up...!) A survey was sent out and only 30% of all 6th~11th grade students said Ms. Tina is cool. Ms. Tina's excuse is that she only knows about 70% of the students, and only 40% of all students who were sent the survey responded.

If we pick a random student who responded to the survey, what is the probability (in percent) that this student responded to the survey with "Ms. Tina is cool"?

(a)  

Based on the statistics in the image from Our World in Data, what is the probability (in percent) that someone is NOT yet fully vaccinated given that they are Taiwanese? Round your answer to the nearest tenth of a percent.

(a)  

The image displays statistics of Taiwan's vaccination rates as of May 6th, 2022. Source: Our World in Data.

What is the probability that a randomly selected fully vaccinated individual has already had their booster?

• 61.4%

• 73.0%

• 77.3%

• 94.4%

CHALLENGE: Ruby chooses one card from a standard deck of 52 cards (no joker). She doesn't like it and puts it back, then picks another one. What is the probability that she chose the same card both times?

(a)  

CHALLENGE: I have a pen, I have an apple.

You have a pen, you have [a] pineapple.

We put these four items in one pile and pick randomly. What is the probability we can make an apple-pen by picking an apple first and then a pen?

• 1/12

• 1/6

• 1/3

• 3/4

CHALLENGE: Arina left a standard deck of 52 cards (no joker) on her table and went to the snack bar. Yoko took away all 6 of the red royals (diamond and heart J, Q, and K) as a joke.

Arina comes back and picks a card from the deck, puts it back, then picks another card. What is the probability that she picks a Queen and then a King?

Leave your answer as a fraction in simplest form with no spaces and a slash in between (eg. "5/6").

(a)