Probabilities of Dependent Events

Probabilities of Dependent Events

Determining probabilities of dependent events is usually more complicated than determining them for independent events.

Probabilities of Dependent Events

Determining probabilities of dependent events is usually more complicated than determining them for independent events.

Since some of the tree diagrams could get very large, we will focus on a quicker method

Probabilities of Dependent Events

Determining probabilities of dependent events is usually more complicated than determining them for independent events.

Since some of the tree diagrams could get very large, we will focus on a quicker method, multiplication.

Probabilities of Dependent Events

Ex.1) Independent Events:

Probabilities of Dependent Events

Ex.1) Independent Events:Spinner #1 is partitioned into three equal sections, coloured black, white, and grey. Spinner #2 is partitioned into four equal sections, coloured red, blue, green, and yellow.

Probabilities of Dependent Events

Ex.1) Independent Events:Spinner #1 is partitioned into three equal sections, coloured black, white, and grey. Spinner #2 is partitioned into four equal sections, coloured red, blue, green, and yellow. If both spinners are spun, what is the probability of getting black and red?

Probabilities of Dependent Events

Ex.1) Independent Events:Spinner #1 is partitioned into three equal sections, coloured black, white, and grey. Spinner #2 is partitioned into four equal sections, coloured red, blue, green, and yellow. If both spinners are spun, what is the probability of getting black and red?

Since we expect to get black one-third of the time, and we expect to get red one-quarter of the time, then we expect to get black and red one-third of one-quarter of the time. . .

Probabilities of Dependent Events

12

14

1

3

14

1

3

1)(

ofredandblackP

Probabilities of Dependent Events

12

14

1

3

14

1

3

1)(

ofredandblackP

Probabilities of Dependent Events

12

14

1

3

14

1

3

1)(

ofredandblackP

Probabilities of Dependent Events

12

14

1

3

14

1

3

1)(

ofredandblackP

Imagine a tree diagram where the first column shows the three outcomes for Spinner #1, each of which is followed by the four outcomes for Spinner #2 in the second column.

Probabilities of Dependent Events

12

14

1

3

14

1

3

1)(

ofredandblackP

Imagine a tree diagram where the first column shows the three outcomes for Spinner #1, each of which is followed by the four outcomes for Spinner #2 in the second column.

Three groups of four branches creates 12 possible outcomes.

Probabilities of Dependent Events

Ex.2) Dependent Events:

Probabilities of Dependent Events

Ex.2) Dependent Events: A bag contains 10 marbles; 5 red, 3 blue, and 2 silver.

Probabilities of Dependent Events

Ex.2) Dependent Events: A bag contains 10 marbles; 5 red, 3 blue, and 2 silver. If you draw one marble at random and hold it in your left hand, and then draw a second marble at random and hold it in your right hand, what is the probability that you are holding two silver marbles?

Probabilities of Dependent Events

Ex.2) Dependent Events: A bag contains 10 marbles; 5 red, 3 blue, and 2 silver. If you draw one marble at random and hold it in your left hand, and then draw a second marble at random and hold it in your right hand, what is the probability that you are holding two silver marbles?

It’s easy to determine the probability of the first marble being silver. However, notice that if you start by getting a silver marble and then try for the second, the bag will be different.

Probabilities of Dependent Events

Ex.2) Dependent Events: A bag contains 10 marbles; 5 red, 3 blue, and 2 silver. If you draw one marble at random and hold it in your left hand, and then draw a second marble at random and hold it in your right hand, what is the probability that you are holding two silver marbles?

It’s easy to determine the probability of the first marble being silver. However, notice that if you start by getting a silver marble and then try for the second, the bag will be different.How?

Probabilities of Dependent Events

Ex.2) Dependent Events: A bag contains 10 marbles; 5 red, 3 blue, and 2 silver. If you draw one marble at random and hold it in your left hand, and then draw a second marble at random and hold it in your right hand, what is the probability that you are holding two silver marbles?

It’s easy to determine the probability of the first marble being silver. However, notice that if you start by getting a silver marble and then try for the second, the bag will be different.How? Now, there is only one silver marble in a bag containing a total of 9 marbles. . .

Probabilities of Dependent Events

45

19

1

5

19

1

10

2)(

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Probabilities of Dependent Events

45

19

1

5

19

1

10

2)(

silverandsilverP

Probabilities of Dependent Events

45

19

1

5

19

1

10

2)(

silverandsilverP