Multiplication rule for "AND"

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

0/1
Intros
Lessons
1. P(A and B) VS. P(A or B)

P(A and B): probability of event A occurring and then event B occurring in successive trials.
P(A or B):
probability of event A occurring or event B occurring during a single trial.
0/5
Examples
Lessons
1. 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?
1. Independent Events VS. Dependent Events
1. 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 $1^{st}$ card is an ace}
B = {the $2^{nd}$ card is an ace}
Determine:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ Are events A, B dependent or independent?
$\cdot$ P(A and B), using both the tree diagram and formula
2. 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 $1^{st}$ card is an ace}
B = {the $2^{nd}$ card is an ace}
Determine:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ Are events A, B dependent or independent?
$\cdot$ P(A and B), using both the tree diagram and formula
2. 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.
1. What is the probability of selecting a green ball from Bag A?
2. What is the probability of selecting a green ball?
Topic Notes
$\cdot$ P(A and B): probability of event A occurring and then event B occurring in successive trials.

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

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

$\cdot$ 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) $\cdot$ P(B | A)
= P(A) $\cdot$ P(B)