AI generatedProbabilityKS3 / GCSE

Adding probabilities across alternative branches

Adding probabilities across alternative branches.

  • At each split, the outgoing probabilities sum to 1.
  • Multiply along a route; add mutually exclusive routes that meet the question.
  • Without replacement, update the counts and total for the second draw.

Example 1

A bag contains 2 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.

Example 2

A bag contains 3 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.

Your turn

Question 1

A bag contains 4 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Check answer
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.
Question 2

A bag contains 5 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Check answer
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.
Question 3

A bag contains 6 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Check answer
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.
Question 4

A bag contains 7 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Check answer
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.
Question 5

A bag contains 8 red and 3 blue counters. Two counters are drawn with replacement, mixing between draws. Find the probability of exactly one red.

Two-stage probability treeFirstSecondRRBBRB
Check answer
Red then blue is one route.Blue then red is a different route.Add these mutually exclusive routes.
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