6th Grade Math Textbook, Fundamentals

Lesson 12-6 for exercise sets. &KDSWHU 

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• A box holds the following letter cards: B L U E.
  Mia picks a card at random and does not replace it in the box.
  Without looking, she picks another card at random. What is the
  probability that Mia will pick a consonant and then a vowel?

Identify the events: A picking a consonant

B picking a vowel

P(A, then B) P(A) P(B after A)

P(A) P(a consonant) 

P(B after A) P(vowel, after a consonant) 

P(consonant, then a vowel)      33 %

Check:Draw a tree diagram to check your answer.

Sample space {(B, L); (B, U); (B, E); (L, B); (L, U); (L, E);

(U, B); (U, L); (U, E); (E, B); (E, L); (E, U)}

Using the sample space, you can confirm that the probability

of picking a vowel after a consonant is  or 33 %.

2

4

number of consonant cards

total number of cards

2

3

number of vowel cards

number of remaining cards

2

4

2

3

4

12

1

3

1

3

4

12

1

3

1

3

Key Concept

Probability of Dependent Events

If A and B are dependent events, then

P(A, then B)P(A) P(B after A).

Explain why the events are either dependent or independent.

1.Rolling an even number on both the 1st and 2nd roll

of a 1–6 number cube

2.Choosing a red rose, not replacing it, and then choosing a

white rose from a vase of 3 white, 2 red, and 6 yellow roses

Find each probability.

A box contains 2 red blocks (R), 1 yellow block (Y), and 1 green block (G).
A block is chosen at random and not replaced. Then another block is chosen.

3.P(R, then Y) 4.P(R, then R) 5.P(G, then G)

A box contains 2 striped blocks (S) and 1 checkered block (C). A block is
chosen at random and replaced. Then another block is chosen.

6.P(S and S) 7.P(S and C) 8.P(one of each)

9.Discuss and Write Describe two events that are independent and two that

are dependent.

L

U

E

B

B

L

E

U

B

U

E

L

B

L

U

E

To find the probability of dependent events, multiply

the probability of the first event by the probability of

the second event, after the first event has occurred.

Think

The first event affects

the probability of the

second event, so the

events are dependent.