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You can use two-way tables to find conditional probabilities. Recall that conditional probability is the probability that some event (B) occurs given that some other event (A) has already occurred. The probability of B given A is written this way:
P(B, given A) = P(B | A)
EXAMPLE
Suppose that 338 middle school students were asked which was their dominant hand. Here the results are shown in the two-way table:
|
Dominant Hand |
|
|||
---|---|---|---|---|---|
Right | Left | Ambidextrous |
|
||
Grade | 6th | 99 | 9 | 2 | 110 |
7th | 90 | 31 | 0 | 121 | |
8th | 93 | 11 | 3 | 107 | |
|
|
282 | 51 | 5 | 338 |
Questions | Written as Conditional Probability | Conditional Probability Formula |
---|---|---|
What is the probability that a seventh-grade student is ambidextrous? | What is the probability that a student is ambidextrous, given they are a seventh grader? | |
What is the probability that a student who is right-handed is in eighth grade? | What is the probability that a student is in eight grade, given that he or she is right-handed? |
You can use a two-way table that actually has probabilities in it or relative frequencies.
EXAMPLE
A class of 10th graders was asked if they prefer cheese, pepperoni, or sausage pizza. The percentages are shown below: 41% of all of these kids are girls that enjoy cheese pizza, 12% of all of the kids are boys that enjoy pepperoni, etc.
|
Cheese | Pepperoni | Sausage |
|
---|---|---|---|---|
Boy | 0.05 | 0.12 | 0.19 | 0.36 |
Girl | 0.41 | 0.16 | 0.07 | 0.64 |
|
0.46 | 0.28 | 0.26 | 1 |
Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.