AI generatedProbabilityCourse skill

Finding exactly two successes in three trials

Finding exactly two successes in three trials.

  • 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

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Multiply along one three-stage route.Add the three equally probable disjoint routes.

Example 2

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Multiply along one three-stage route.Add the three equally probable disjoint routes.

Your turn

Question 1

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Check answer
Multiply along one three-stage route.Add the three equally probable disjoint routes.
Question 2

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Check answer
Multiply along one three-stage route.Add the three equally probable disjoint routes.
Question 3

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Check answer
Multiply along one three-stage route.Add the three equally probable disjoint routes.
Question 4

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Check answer
Multiply along one three-stage route.Add the three equally probable disjoint routes.
Question 5

Three independent trials each have success probability . Find .

The three disjoint routes with exactly two successes
RouteProbability
SSF
SFS
FSS
Check answer
Multiply along one three-stage route.Add the three equally probable disjoint routes.
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