Conditional probabilities
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A conditional probability is the probability that an event occurs, given that another has occurred.
P(A | B) is the same as P(A given B)!
Scenario: Consider the table below detailing Delta Apple Pi's bid breakdown from this year's rush season. Calculate the probability of a recruit receiving a bid given that they wore a hat.
| Received bid | Did not receive bid | ||
|---|---|---|---|
| Wore a hat | 15 | 60 | 75 |
| Did not wear a hat | 25 | 100 | 125 |
| 40 | 160 | 200 |
| Clue | Insight |
|---|---|
| We're assessing the probability of an event happening (receiving a bid) given that another event has occurred (wore a hat). | ...meaning this is a conditional probability. |
Conditional Probability = Cell Value / Row or Column Total
Received bid & Wore a hat = 15
Total for Wore a hat = 75
P(Received Bid | Wore a hat) = 15 / 75
P(Received Bid | Wore a hat) = 0.2
Answer: The probability of a recruit receiving a bid given that they wore a hat is 0.2.
Mathematically...
P(A | B) = P(A ∩ B) / P(B)
| Received bid | Did not receive bid | ||
|---|---|---|---|
| Wore a hat | 15 | 60 | 75 |
| Did not wear a hat | 25 | 100 | 125 |
| 40 | 160 | 200 |
Received Bid & Wore a hat = 15
Wore a hat = 75
Grand Total = 200
P(Received bid ∩ Wore a hat) = 15 / 200
P(Received bid ∩ Wore a hat) = 0.075
P(Wore a hat) = 75 / 200
P(Wore a hat) = 0.375
P(Received bid | Wore a hat) = 0.075 / 0.375
P(Received bid | Wore a hat) = 0.2
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Question 1 of 2
1. Question
What type of probability could we consider a student making junior varsity, given they’re a freshman?
Freshman Sophomore Junior Senior Made Varsity 2 3 8 9 22 Made Junior Varsity 8 12 3 0 23 Got cut 3 4 1 1 9 13 19 12 10 54 CorrectIncorrect -
Question 2 of 2
2. Question
Solve for the probability of a student making junior varsity, given they’re a freshman.
Freshman Sophomore Junior Senior Made Varsity 2 3 8 9 22 Made Junior Varsity 8 12 3 0 23 Got cut 3 4 1 1 9 13 19 12 10 54 CorrectIncorrect