Independent and Dependent Events - Probability

Independent and Dependent Events - Probability

Independent & Dependent Events

• Independent - One activity does not effect the outcome of a different activity. (Drawing marbles from a bag and then putting them back in the bag each time before you draw again.)

• Dependent - One activity DOES effect the outcome of another activity. (Drawing a card from a deck of cards and NOT putting it back in the stack before you draw another one.)

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.

P(spinning an odd number) ⋅ P(flipping a coin on tails) = 3/5 ⋅ 1/2

= 3/10 or 30%

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 there with 5 of your relatives and 6 other friends. What is the probability that one of your relatives is chosen first, and then one of your friends is chosen second?

P(relative chosen 1st) ⋅ P(friend chosen 2nd) = 5/100 ⋅ 6/99 = 30/9900

= 0.003 or 0.3%

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 for landing on 2 heads and 1 tail : HHT, HTH, and THH.

P(2 heads and 1 tails) =

number of favorable outcomes

sample space

= 3/8 = 0.375 or 37.5%

Remember,

sample space is the total number of possible outcomes

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 the table to find the sample space.

P(greater than 4 and tails) =

number of favorable outcomes

sample space

= 2/12 = 1/6

= 0.167 or 16.7%

Fill in the Blank

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

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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.