## Multiplication Rule of Probability

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-CP.B.8

What is the Multiplication Rule of Probability? If you remember, we discussed probability and its rules quite in-depth. With the concept of probability taking the center position in statistics, learning about its rules are as important as learning about the concept. If the probability is something you find difficult and fear to deal with, we tell you that if you learn about its rules, you will get a better grasp at understanding probability. The multiplication rule states that: P(A and B) = P(A) * P(B|A) or P(B) * P(A|B) In the above rule, if A and B are two independent events, the formula can be shrunk to; P(A and B) = P(A) * P(B) Independent events refer to the events whose outcome is not affected by the occurrence or happening of another event. For instance, if two coins are flipped together, the second flip might have a chance of 0.50% of landing heads, regardless of the outcome in the first flip. What's the probability of having tails in the first flip and heads in the second when you flip the coins twice? A large selection of lessons and worksheets that show students how to use and apply the use of the Multiplication Rule of Probability.

### Printable Worksheets And Lessons

- Bag of Candy Step-by-step Lesson- What is the chance of getting a green candy out of a mixed bag.
- Guided Lesson - Marbles, pulling cards from a deck, and colored papers.
- Guided Lesson Explanation - It is also helpful to draw images along with the values.
- Practice Worksheet - What's the chances?
- Matching Worksheet - Sorry, so of these problems are a bit long winded.

#### Homework Sheets

We see several different form of probability floating around these problems.

- Homework 1 - Kitty has a bag of toys. In the bag there are 6 blue colored toys, 4 white colored toys and 9 purple colored toys. She takes one toy and records its color. She then puts it back in the bag. She then draws another color toy. What is the probability of taking out a blue colored toy followed by the white colored toy?
- Homework 2 - Cheri has a box with 8 blue balls and 4 red balls. Two balls are drawn without replacing them in the box. What is the probability that both of the balls are blue?
- Homework 3 - David has a basket of caps. In the basket there are 6 red caps, 3 yellow caps and 7 green caps. He takes one cap and records its color and puts it back in the basket. He then draws another cap. What is the probability of taking out a yellow caps followed by the red cap?

#### Practice Worksheets

You will find a mix of 3, 4, and 5 variables in these problems.

- Practice 1 - Mia has a box of pencils. In the box there are 12 red pencils, 14 yellow pencils and 10 green pencils. She takes one pencil records its color and puts it back in the box. She then draws another pencil. What is the probability of taking out a red pencil followed by a green pencil?
- Practice 2 - Julia has a bag with 10 pink hankies and 8 white hankies. Two hankies are drawn without replacement from the bag. What is the probability that both of the hankies are white?
- Practice 3 - Liam has a box of caps. In the box there are 6 yellow caps, 8 green caps and 10 blue caps. He randomly takes one cap out of the box. He records its color and puts it back in the box. He then draws another cap. What is the probability of taking out a blue cap followed by a yellow cap?

#### Math Skill Quizzes

Make sure you pay attention to if the item is replaced after it is chosen.

- Quiz 1 - Jacob has a bag of hair bands. In the bag there are 10 red hair bands, 9 green hair bands and 5 orange hair hands. He takes one hair band out, records its color hair band and puts it back in the bag. He then draws another hair band. What is the probability of taking out a red hair band followed by the green hair band?
- Quiz 2 - Lima has a box with 10 orange pens and 8 blue pens. Two pens are drawn without replacement from the box. What is the probability that both of the pens are orange?
- Quiz 3 - Alex has a box of mobile phones. In the box there are 5 green mobiles, 10 red mobiles and 8 pink mobiles. He takes one mobile, records its color and puts it back in the box. He then draws another mobile phone. What is the probability of taking out a red mobile followed by the pink mobile?