Year 9 Probability: Tree Diagrams

You are completing a multiple-choice test, each answer is labelled {a, b, c, d}, there are 2 questions for the multiple choice test.

What is the probability that A is the correct answer for both questions?

Mathematical Equivalence

ON

Answer explanation

The probability for any of the answers are 1/4

So for a two step experiment:

1/4 x 1/4 = 1/16

You are completing a multiple-choice test, each answer is labelled {a, b, c, d}, there are 4 questions for the multiple choice.

What is the probability that the answer to the first question is A and the second question is B.

Mathematical Equivalence

ON

Answer explanation

Same principle applies from the previous question.

Each question has a 1/4 probability of being correct.

1/4 x 1/4 = 1/16

You are completing a multiple-choice test, each answer is labelled {a, b, c, d}, there are 4 questions for the multiple choice.

What is the probability of choosing the answer C in both questions and answering D in both questions

Mathematical Equivalence

ON

Answer explanation

Recall that when finding more than one outcome you add both outcomes together

So the probability of both being C is 1/4 x 1/4 = 1/16

Same principle applies for both answers being D

So 1/16 + 1/16 = 2/16 = 1/8

A game involves tossing two coins. Complete a tree diagram to show all possible outcomes and find the probability of tossing exactly two heads.

Mathematical Equivalence

ON

Answer explanation

Pr(Heads) = 1/2

• Tossing the coin two times in a row results in Pr(Heads) X Pr(Heads) = 1/2 x 1/2

A bag contains 5 red cards, 3 blue cards, and 2 green cards. A student randomly selects one card from the bag, notes its color, and then, without replacement, selects another card.

What is the probability that the first card is blue and the second card is green?

Mathematical Equivalence

ON

Answer explanation

Pr(Blue) = 3/10

Pr(Green (In second pick) = 3-1/10-1 = 2/9

3/10 x 2/9 = 2/30 = 1/15

A bag contains 5 red cards, 3 blue cards, and 2 green cards. A student randomly selects one card from the bag, notes its color, and then, without replacement, selects another card.

Find the probability that both cards are red.

Mathematical Equivalence

ON

Answer explanation

Pr(Red) = 5/10 or 1/2

Pr(Red (in second pick) = 5-1/10-1 = 4/9

1/2 x 4/9 = 2/9

When we want to find the probability of two or more outcomes. We ​ (a)   the outcomes together.

• add
• subtract

​ (a)   replacement involves the decrease of the ​ (b)   and the ​ (c)   by 1.

• Without
• With
• sample space
• chosen outcome
• many outcomes
• probabilities

Match the following:

• Pr(AB) + Pr(CC)

• The probability of choosing C and C

• Pr(A) x Pr(B)

• All probabilities in one round/branch equal to:

• Pr(C) x Pr(C)

• The probability of more than one outcome is

• 1

• The probability of choosing A then B is:

There are three blocks of lego, a blue block, a yellow block and red block. I pick one of these blocks and put them back. I do this three times.

What is the probability that I pick a red block and two blue blocks in a row?

Mathematical Equivalence

ON