Conditional probability - Probability

Conditional probability

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Notes:

$\cdot$ P(B | A): probability of event B occurring, given that event A has already occurred.

$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B | A)

then: P(B | A) = $\frac{P(A\;and \;B)}{P(A)}$

1.
Probability Tree Diagram
Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;

if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.

Conditional probability

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Notes:

⋅\cdot⋅ P(B | A): probability of event B occurring, given that event A has already occurred. ⋅\cdot⋅ recall: P(A and B) = P(A) ⋅\cdot⋅ P(B | A) then: P(B | A) = P(AandB)P(A)\frac{P(A\;and \;B)}{P(A)}​P(A)​​P(AandB)​​

Intro Lesson

Definition of Conditional Probability ⋅\cdot⋅ P(B | A): probability of event B occurring, given that event A has already occurred. ⋅\cdot⋅ recall: P(A and B) = P(A) ⋅\cdot⋅ P(B | A) then: P(B | A) = P(AandB)P(A)\frac{P(A\;and \;B)}{P(A)}​P(A)​​P(AandB)​​

1.

Probability Tree Diagram Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls. A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A; if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.

a)

Find the probability that a red ball is selected.

b)

Given that the ball selected is red, find the probability that it came from Bag A.

2.

It is known that 60% of graduating students are girls. Two grads are chosen at random. Given that at least one of the two grads are girls, determine the probability that both grads are girls.

Conditional probability

Don't just watch, practice makes perfect.

We have over 310 practice questions in Statistics for you to master.

or

$\cdot$ P(B | A): probability of event B occurring, given that event A has already occurred.

$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B | A)

then: P(B | A) = $\frac{P(A\;and \;B)}{P(A)}$

Definition of Conditional Probability
$\cdot$ P(B | A): probability of event B occurring, given that event A has already occurred.

$\cdot$ recall: P(A and B) = P(A) $\cdot$ P(B | A)

then: P(B | A) = $\frac{P(A\;and \;B)}{P(A)}$

Probability Tree Diagram
Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;

if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.