Dependent events depend on the actions of the previous event. The result of one event has an impact on other events.

Dependent events using "and"

Use the formula: P(A and B) =P(A) x P(B, given A)

For example: If you have three red marbles, and three blue marbles. What are the chances of picking a blue marble, and then a red marble? Because the marbles are not replaced each time, there is a smaller number of marbles which will impact the next event.

Independent events using "or"

Use the formula: P(A or B ) = P(A) + P(B)

For example:

What is the probability of rolling a 5 the first roll, or a 6 the second time?

1/6 + 1/6 =2/6 =1/3

Roll 1 Roll 2

add the fractions because it is an "or" event

Therefore, you will have a 1/3 chance of rolling a 5 or a 6

Independent events involving “and”

When you have independent events along with the statement “and” use the formula

P(A and B) = P(A) x P(B)

Please note P( ) means the probability of an event. The event is placed in the ( ) for example

What is the probability of rolling a 5 on a six sided die can be written P(5)

1. Use this formula: Positive Outcomes

Total Outcomes

2. Reduce the fraction for your probability.

3. In order to convert it to a percent, divide the numerator ( top number) by the denominator ( bottom number) and multiply by 100.

Example 1 : If you have 5 red marbles, 2 blue marbles, and 3 green marbles. What is the probability you will pick a green marble?

Step 1. Use the formula:

Step 2. Divide the numerator by the denominator 3/10 = .3

Step 3. Multiply by 100 to get the percent. .3 x 100 = 30 %

Independent Events: Events are independent if the result of the second event is not affected by the actions of the first event.

You may think of independent events as isolated events.

For example: Flipping a coin. Each flip of the coin has no impact on the next flip.

If you have three red marbles, and three blue marbles placed on a table. What are the chances of picking a blue marble, and then a red marble if the marbles are replaced each time? Because the marbles are replaced each time they have no bearing on the next event.

Probability of Dependent Events

Becky has a deck cards. What is the probability that she will draw a face card, then a red card with out replacement?

Probability of “or” with dependent events.

P(A or B ) = P(A) + P(B) – P(A and B )

Bob has several shirts of different colors. In a box he has 2 yellow with pockets, 2 red, 4 white with pockets, and 2 black.

What is the probability of randomly picking a white shirt, or a black shirt.

What is the probability of randomly choosing a star from Group 1, and an arrow from group 2?

Step 1. Multiply the probability of the group 1 times the probability of group 2. Group one has four stars, and seven total objects. Group two has three arrows out of six objects total.

4/7 x 3/6

Step 2. With "and" problems you multiply

4/7 x 1/2 = 4/14

Step 3. Reduce the fraction

= 2/7

= 2 ÷ 7

= 0.285714

0.285714 x 100 = 28.5714%

The probability of choosing a star and an arrow equals 28.57%.

Video Tutorial Probability of Independent Events

What is the probability of choosing a white shirt, or a shirt with a pocket?

4/10 +2/10 =6/10

=3/5 = .60

= .60 *100 = 60%

4/10+6/10-4/10= 6/10

=3/5= .60

=.60*100 = 60%

Video Answer to the last two problems

3/6 x 3/5 =9/30 =3/10= 30%

You do not replace the marbles each time so when you make the second pick you only have 5 marbles.

12/52 x12/51 = 144/2652

= 12/221 = .o542

= .0542 x 100 = 5.42%

Video Solution to Dependent events with "and"

What is probability? In simple terms it is how " likely" an event will occur. For instance, if you flip a coin how likely is it you will flip a heads ? In order to calculate probability follow these steps. span>