Independent and Dependent Probability

INdependent and DEpendent events

(in math)

Multiple Choice

Jazlyn has 4 quarters, 10 dimes, and 3 nickels in her wallet. What is the likelihood of her choosing a penny?

• certain

• likely

• unlikely

• impossible

Multiple Choice

If you roll a 6-sided die, what is the probability of rolling a two?

• 2/6

• 1/6

• 1/3

• 1/5

Multiple Choice

If a stone is dropped at random on the arrangement of tiles shown, what is the probability the stone will not land on a white tile?

• 5/9
• 4/9
• 1/2
• 1/9

Multiple Choice

Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?

• Yes

• No

Independent Events

● The outcome of one event will NOT affect the outcome of

another event.

● Example

■ Flipping a coin and rolling a 6 sided die

Dependent Events

● The outcome of the first event will change the probability of

the second event.

● Example

○ Drawing out an item then drawing out another one

WITHOUT returning the first

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then without putting the first card back, she picks a second card at random.

• Independent

• Dependent

Multiple Choice

You want to draw a heart and then draw another heart.

You draw the first card, look at it, put it back in the deck and draw another card. Are these independent or dependent compound events?

• dependent

• independent

Multiple Choice

You want to draw two aces. You draw one card, look at it, keep it out and draw another card. Are these independent or dependent compound events?

• independent

• dependent

Fill in the Blank

You pick a marble and pick a card. How many outcomes are possible?

Calculate more than one independent event

1) Calculate the probability of EACH event
2) MULTIPLY the probability of each event together

Calculate more than one independent event

What is the probability of rolling a die 3 time and it being 1 each time?

Multiple Choice

Suppose a number cube is rolled twice. What is the probability that an odd number will show both times?

• 1/3

• 1/2

• 1/6

• 1/4

Multiple Choice

What is the probability of tossing a coin four times and getting tails each time?

• 1/16

• 1/8

• 1/2

• 1/4

Multiple Choice

Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.

• 27/180 or 3/20

• 45/180 or 1/4

• 63/180 or 3/31

• 81/180 or2/27

Multiple Choice

Tyler has a 80% chance of making a free throw. What is the probability that Tyler makes the next 2 free throws?

• 64%

• 80%

• 16%

• 100% because Tyler has been practicing

Multiple Choice

Predict how many times the spinner will land on green if the spinner is spun 120 times.

• 40

• 50
• 25
• 10

Multiple Choice

On a game show, contestants randomly choose a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 3/10 (30%). The bag contains 9 strikes. How many chips are in the bag?

• 27
• 15
• 20
• 30

Calculate more than one dependent event

- Steps are the same BUT you have to remember that the

2nd event will have, at least, a different denominator
than the first.

1)

Calculate the probability of EACH event

2)

MULTIPLY the probability of each event together

Calculate more than one dependent event

​What is the probability of picking 2 aces out of a deck of 52 cards WITHOUT putting the 1st card back?

Multiple Choice

When randomly drawing from a standard deck of 52 playing cards, what is the probability of drawing a 9 four times in a row if the cards are not replaced?

• 1/5,525

• 1/270,725

• 1/28,561

• 1/4

Multiple Choice

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a quarter, not replacing it, and then picking a penny?

• 20/121

• 8/121

• 2/11

• 4/55

Multiple Choice

You are playing a game of scrabble. The tiles shown are dropped in a bag. You need to choose a tile. What is the probability of choosing either an "E" OR an "H"?

• 4/15

• 1/70

• 1/75

• 3/225

Multiple Choice

You are playing a game of scrabble. The tiles shown are dropped in a bag. You need to choose two tiles. What is the probability of choosing an "E", keeping it, and then choosing a "H"?

• 4/15

• 1/70

• 1/75

• 1/225

Math Response

Find P(red marble with replacement, then black marble).

Answer as a fraction

Type answer here

Correct Answer: \frac{1}{50}

Deg^°

Rad

Math Response

A farm has 5 brown cows and 10 white cows. A fence is open and two cows escape. What is the probability that it will be a brown cow, then a white cow?

Answer as a fraction

Type answer here

Correct Answer: \frac{5}{21}

Deg^°

Rad

Math Response

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick two marbles without looking, what is the probability that the marble you pick will be red or blue and then without replacing it a pink.

answer as a fraction

Type answer here

Correct Answer: \frac{5}{33}

Deg^°

Rad

Fill in the Blank

There is a 60% chance that a male will rent a car. What is the probability that the next customer is a man that will rent a Convertible or SUV?

(answer as a percent)