What is the quickest way to calculate probability?

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.

Are there harder ways to do this type of question?

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.

Is there any formula for conditional probability, or is it simply common sense? (in general questions)

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!

Why shouldn't we apply Bayes theorem in question 3 (P(male ∣ fly))?

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.

What's the difference between P(male and fly) and P(male | fly)??

P(male | fly) = the probability that the student is male given that the student chose to fly as their superpower

How did you get your answer that 62% of females chose invisibility as their superpower. I saw up above, it was 44.

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%

Main content

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 7

Lesson 3: Conditional probability

Conditional probability using two-way tables

AP.STATS:

VAR‑4 (EU)

VAR‑4.D (LO)

VAR‑4.D.1 (EK)

CCSS.Math:

HSS.CP.A.4

HSS.CP.B.6

Google Classroom

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.

problem 1

Find the probability that the student chose to fly as their superpower.

P, left parenthesis, start text, f, l, y, end text, right parenthesis, equals

problem 2

Find the probability that the student was male.

P, left parenthesis, start text, m, a, l, e, end text, right parenthesis, equals

problem 3

Find the probability that the student was male, given the student chose to fly as their superpower.

P, left parenthesis, start text, m, a, l, e, space, end text, vertical bar, start text, space, f, l, y, end text, right parenthesis, equals

problem 4

Find the probability that the student chose to fly, given the student was male.

P, left parenthesis, start text, f, l, y, space, end text, vertical bar, start text, space, m, a, l, e, end text, right parenthesis, equals

problem 5

Is this statement about conditional probability true or false?

"In general, P, left parenthesis, start text, A, space, end text, vertical bar, start text, space, B, end text, right parenthesis, equals, P, left parenthesis, start text, B, space, end text, vertical bar, start text, space, A, end text, right parenthesis. You can reverse the order and the probability is the same either way."

problem 6

Let start text, I, end text represent the event where the student chose invisibility as their superpower, and start text, F, end text represent the event where the student was female.

Interpret the meaning of P, left parenthesis, start text, I, space, end text, vertical bar, start text, space, F, end text, right parenthesis, approximately equals, 0, point, 62.

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Mike Wallace
Posted 7 years ago. Direct link to Mike Wallace's post “How did you get your answ...”
How did you get your answer that 62% of females chose invisibility as their superpower. I saw up above, it was 44.
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(0 votes)
Answer
- Christian Montecillo
  Posted 7 years ago. Direct link to Christian Montecillo's post “44 is the TOTAL number of...”
  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%
  Button navigates to signup page
  (10 votes)
Ana Duran Martinez
Posted 5 years ago. Direct link to Ana Duran Martinez's post “I might need to practice ...”
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!
Button navigates to signup pageComment on Ana Duran Martinez's post “I might need to practice ...”
(23 votes)
Answer
dwear
Posted 5 years ago. Direct link to dwear's post “What is the quickest way ...”
What is the quickest way to calculate probability?
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(3 votes)
Answer
- jerfersondossantosdematos
  Posted 5 years ago. Direct link to jerfersondossantosdematos's post “in a bag with six things ...”
  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.
  Button navigates to signup page
  (2 votes)
manvir.sandhu
Posted 5 years ago. Direct link to manvir.sandhu's post “Are there harder ways to ...”
Are there harder ways to do this type of question?
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(3 votes)
Answer
- nina.groleger
  Posted 5 years ago. Direct link to nina.groleger's post “I think Bayes' Theorem qu...”
  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.
  Comment on nina.groleger's post “I think Bayes' Theorem qu...”
  (3 votes)
Ahmad MJ
Posted 4 months ago. Direct link to Ahmad MJ's post “I honestly don't understa...”
I honestly don't understand this, Thank you for making all this content available.
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(3 votes)
Answer
Ivanshi Gadani
Posted 3 months ago. Direct link to Ivanshi Gadani's post “Is there any formula for ...”
Is there any formula for conditional probability, or is it simply common sense? (in general questions)
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(1 vote)
Answer
- Ian Pulizzotto
  Posted 3 months ago. Direct link to Ian Pulizzotto's post “In general, if A and B ar...”
  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!
  Button navigates to signup page
  (3 votes)
balaloganathan1
Posted 4 years ago. Direct link to balaloganathan1's post “the correct answer given ...”
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?
Button navigates to signup pageComment on balaloganathan1's post “the correct answer given ...”
(2 votes)
Answer
kevin_prabha
Posted 4 years ago. Direct link to kevin_prabha's post “Why shouldn't we apply Ba...”
Why shouldn't we apply Bayes theorem in question 3 (P(male ∣ fly))?
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(1 vote)
Answer
- Jerry Nilsson
  Posted 4 years ago. Direct link to Jerry Nilsson's post “Bayes' Theorem says P(mal...”
  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.
  Comment on Jerry Nilsson's post “Bayes' Theorem says P(mal...”
  (2 votes)
He Sheng Xin
Posted 2 years ago. Direct link to He Sheng Xin's post “What's the difference bet...”
What's the difference between P(male and fly) and P(male | fly)??
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(1 vote)
Answer
- astro648
  Posted 2 years ago. Direct link to astro648's post “P(male | fly) = the proba...”
  P(male | fly) = the probability that the student is male given that the student chose to fly as their superpower
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  (2 votes)
averynash
Posted 6 years ago. Direct link to averynash's post “In problem #3, when using...”
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.
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(1 vote)
Answer
- Mark Geary
  Posted 6 years ago. Direct link to Mark Geary's post “Of the 38 students who ch...”
  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!
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  (1 vote)