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## AP®︎/College Statistics

### Course: AP®︎/College Statistics > Unit 7

Lesson 3: Conditional probability- Conditional probability and independence
- Conditional probability with Bayes' Theorem
- Conditional probability using two-way tables
- Calculate conditional probability
- Conditional probability and independence
- Conditional probability tree diagram example
- Tree diagrams and conditional probability

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# Conditional probability using two-way tables

Researchers surveyed 100 students on which superpower they would most like to have. This two-way table displays data for the sample of students who responded to the survey:

Superpower | Male | Female | TOTAL |
---|---|---|---|

Fly | 26 | 12 | 38 |

Invisibility | 12 | 32 | 44 |

Other | 10 | 8 | 18 |

TOTAL | 48 | 52 | 100 |

A student will be chosen at random.

## Want to join the conversation?

- How did you get your answer that 62% of females chose invisibility as their superpower. I saw up above, it was 44.(0 votes)
- 44 is the TOTAL number of people who chose invisibility. Out of those, 32 are female, therefore 32 is the condition that satisfies our probability question (the numerator in the probability formula).

52 is the total number of people who are female in this experiment.

32/52 is about 0.62 or 62%(10 votes)

- I might need to practice this more at home and to read my notes more carefully. It's not easy, but I'll take it as a challenge!(23 votes)
- What is the quickest way to calculate probability?(3 votes)
- in a bag with six things in which two things are pens, what is the probability of you hitting a pen by putting your hand on the bag without looking at it's inside?

you just need to divide the number of pens from the number of things, that is gonna be 2/6 # two pens divided by six things, or you can simplify and you get 1/3, so you have 1/3 probability of hitting a pen.(2 votes)

- Are there harder ways to do this type of question?(3 votes)
- I think Bayes' Theorem questions can get a lot harder than this. We're being given all the information here, so it's easy to calculate any kind of probability, but it gets harder when you don't have all the information and you have to extrapolate.(3 votes)

- I honestly don't understand this, Thank you for making all this content available.(3 votes)
- the correct answer given is 0.2; whereas I gave the answer as 20%; and I got a response that I should try again. Why would you not allow for answers to be presented in fraction or percentage?(2 votes)
- Why shouldn't we apply Bayes theorem in question 3 (P(male ∣ fly))?(1 vote)
- Bayes' Theorem says

P(male | fly) = P(fly | male) ∙ P(male)∕P(fly)

But we don't know what P(fly | male) is, so we can't use this formula.(2 votes)

- What's the difference between P(male and fly) and P(male | fly)??(1 vote)
- P(male | fly) = the probability that the student is male given that the student chose to fly as their superpower(2 votes)

- Is there any formula for conditional probability, or is it simply common sense? (in general questions)(1 vote)
- In general, if A and B are events such that P(B) is nonzero, then

P(A given B) = P(A and B) / P(B).

Have a blessed, wonderful day!(2 votes)

- In problem #3, when using the formula to get the final answer, why is P ( male and fly ) equal to 0.26? I thought that the P ( male and fly ) would be equal to

P (male) * P(fly) = 0.48 * 0.38 which is approximately equal to 0.18. I know I'm doing something wrong, I just can't figure out what.(1 vote)- Of the 38 students who chose (fly) as their superpower, 26 were male. Given the subset of students who chose fly, what percentage are male?

It's semantics, but you have to read the questions carefully.

Hint: the correct answer is between 0.65 and 0.70. Good luck!(1 vote)