Conditional probability worksheets

"Given that it is round" is not extra information, it is a smaller bag. These free printable worksheets ask for a probability after the sample space has been narrowed, which is the move that makes conditional probability different from every probability before it.

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Conditional probability

$Conditional probability worksheet — Two attributes, exact fractions, free printable with answer key$

The answer key prints on a separate page.

What's on this sheet

The commonest wrong answer here is not an arithmetic slip, it is the right fraction over the wrong total. A student who divides by the whole bag has answered "what is the chance it is red AND round" — a real question, and not the one asked. So the worked answer key counts the narrowed group first and never writes the original total down at all.

Why this sheet works

Both directions of each pair appear. P(red given it is round) and P(round given it is red) come off the same bag and are different numbers, and a page that only ever asked one way would let a student believe they are interchangeable. They are equal only when the two things are independent, which is the next idea along.

How this one works

P(round, given it is red) from red 4 round, 3 square · blue 2 round, 3 square

4 + 3=7

4/7

"Given it is red" throws the rest of the bag away. Only the red counters can happen now, so count THOSE: 4 + 3 = 7. That is the new bottom.
Of those 7, 4 are what the question asks for.
4 out of 7, and 4/7 is already in simplest form.

ProbabilityP(given that)

Name: Date:

One counter is drawn. Given what it is, write the probability.

red 4 round, 3 square · blue 2 round, 3 square

P(round, given it is red)

red 2 round, 3 square · blue 4 round, 3 square

P(red, given it is round)

red 3 round, 2 square · blue 5 round, 2 square

P(red, given it is round)

red 3 round, 2 square · blue 3 round, 4 square

P(blue, given it is square)

red 3 round, 2 square · blue 4 round, 3 square

P(square, given it is blue)

red 3 round, 3 square · blue 4 round, 2 square

P(blue, given it is square)

ProbabilityP(given that)

Name: Date:

One counter is drawn. Given what it is, write the probability.

red 3 round, 4 square · blue 2 round, 3 square

P(round, given it is red)

red 2 round, 2 square · blue 5 round, 3 square

P(square, given it is blue)

Probability · P(given that)Answer key

1. red 4 round, 3 square · blue 2 round, 3 square → P(round, given it is red) = 4/72. red 2 round, 3 square · blue 4 round, 3 square → P(red, given it is round) = 1/33. red 3 round, 2 square · blue 5 round, 2 square → P(red, given it is round) = 3/84. red 3 round, 2 square · blue 3 round, 4 square → P(blue, given it is square) = 2/35. red 3 round, 2 square · blue 4 round, 3 square → P(square, given it is blue) = 3/76. red 3 round, 3 square · blue 4 round, 2 square → P(blue, given it is square) = 2/57. red 3 round, 4 square · blue 2 round, 3 square → P(round, given it is red) = 3/78. red 2 round, 2 square · blue 5 round, 3 square → P(square, given it is blue) = 3/8

Conditional probability worksheets

What's on this sheet

How this one works

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