Probability of Independent Events

Independent and Dependent Events - Probability

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Independent & Dependent Events

• Independent - One activity does not effect the outcome of a different activity. (Drawing marbles from a bag, but putting them back each time.)

• Dependent - One activity DOES effect the outcome of another activity. (Drawing a card from a deck of cards, not putting it back and drawing another.)

Multiple Select

You roll a number cube twice. The first time is a 3 and the second time is an even number.

• Independent

• Dependent

Multiple Select

You randomly draw a marble from a bag of marbles. You get a red and don't put it back into the bag. You draw another marble out of the bag and get a yellow.

• Independent

• Dependent

Probability of an Independent Event

Use the formula for the probability of independent events.

P(A and B) = P(A)⋅P(B)

Example: Find the probability of spinning an odd number on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

Multiple Choice

Find the probability of spinning a 2 on a spinner numbered 1 - 5; and the probability of flipping a coin and landing on tails.

• 1/10 or 10%

• 1/4 or 25%

• 1/2 or 50%

• 2/3 or 67%

Probability of a Dependent Event

The probability of two dependent events A and B is the probability of A times the probability of B after A occurs.

P(A and B) = P(A)⋅P(B after A)

People are randomly chosen to be game show contestants from an audience of 100 people. You are with 5 of your relatives and 6 other friends. What is the probability that one of your relatives is chosen fi rst, and then one of your friends is chosen second?

Multiple Choice

People are randomly chosen to be game show contestants from an audience of 100 people. You are with 5 of your relatives and 6 other friends. What is the probability that you, your relatives, and your friends are not chosen to be either of the first two contestants?

• 50/70 or 71.4%

• 58/75 or 77.3%

• 60/70 or 85.7%

• 88/100 or 88%

Tree Diagram

Flipping a coin and landing on heads or tails. There are three favorable outcomes in the sample space: HHT, HTH, and THH.

P(2 heads and 1 tails) =

Fill in the Blank

What is the probability of flipping at least two tails?

Table Diagram

You roll a number cube and flip a coin. What is the probability of rolling a number greater than 4 and flipping tails? Use a table to find the sample space.

P(greater than 4 and tails)

Fill in the Blank

What is the probability of rolling at most 4 and flipping heads?

Poll

How well do you think you understand compound probability?

• I got it, no problem!

• I'm getting there but need some practice.

• I'm struggling, but think I'm on the right path.

• I am really struggling and would like some more instruction.