Multiplication rule for "AND"
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- Multiplication Rule for "AND"
A coin is tossed, and then a die is rolled.
What is the probability that the coin shows a head and the die shows a 4? - Independent Events VS. Dependent Events
- One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.
Consider the following events:
A = {the 1st card is an ace}
B = {the 2nd card is an ace}
Determine:
⋅ P(A)
⋅ P(B)
⋅ Are events A, B dependent or independent?
⋅ P(A and B), using both the tree diagram and formula - One card is drawn from a standard deck of 52 cards and is replaced. A second card is then drawn.
Consider the following events:
A = {the 1st card is an ace}
B = {the 2nd card is an ace}
Determine:
⋅ P(A)
⋅ P(B)
⋅ Are events A, B dependent or independent?
⋅ P(A and B), using both the tree diagram and formula
- One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.
- 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.
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Topic Notes
⋅ P(A and B): probability of event A occurring and then event B occurring in successive trials.
⋅ P(B | A): probability of event B occurring, given that event A has already occurred.
⋅ P(A and B) = P(A) ⋅ P(B | A)
⋅ Independent Events
If the events A, B are independent, then the knowledge that event A has occurred has no effect on the probably of the event B occurring, that is P(B | A) = P(B).
As a result, for independent events: P(A and B) = P(A) ⋅ P(B | A)
= P(A) ⋅ P(B)
⋅ P(B | A): probability of event B occurring, given that event A has already occurred.
⋅ P(A and B) = P(A) ⋅ P(B | A)
⋅ Independent Events
If the events A, B are independent, then the knowledge that event A has occurred has no effect on the probably of the event B occurring, that is P(B | A) = P(B).
As a result, for independent events: P(A and B) = P(A) ⋅ P(B | A)
= P(A) ⋅ P(B)
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