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A coin is flipped and a number cube is rolled. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions.
(a) How many outcomes are there?

◻ outcome(s)
(b) How many outcomes involve rolling a 2 or a 3 ?

◻ outcome(s)
(c) How many outcomes involve tails and an odd number?

◻ outcome(s)

A coin is flipped and a number cube is rolled. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions. $\newline$ (a) How many outcomes are there? $\newline$ $\square$ outcome(s) $\newline$ (b) How many outcomes involve rolling a $2$ or a $3$ ? $\newline$ $\square$ outcome(s) $\newline$ (c) How many outcomes involve tails and an odd number? $\newline$ $\square$ outcome(s)

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Experimental probability

Full solution

Q. A coin is flipped and a number cube is rolled. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions.

\newline

(a) How many outcomes are there?

\newline

\square

outcome(s)

\newline

(b) How many outcomes involve rolling a

2

or a

3

?

\newline

\square

outcome(s)

\newline

(c) How many outcomes involve tails and an odd number?

\newline

\square

outcome(s)

Count Total Outcomes: Count the total number of outcomes in the tree diagram. Since a coin has $2$ sides (Heads, Tails) and a number cube has $6$ sides ( $1$ to $6$ ), each coin outcome pairs with each cube outcome. Calculation: $2$ (coin outcomes) $\times$ $6$ (cube outcomes) $= 12$ total outcomes.
Identify $2$ or $3$ Outcomes: Identify outcomes where the number rolled is either a $2$ or a $3$ . Each of these numbers can occur with either Heads or Tails, so there are $2$ outcomes for rolling a $2$ (Heads with $2$ , Tails with $2$ ) and $2$ outcomes for rolling a $3$ (Heads with $3$ , Tails with $3$ ). Calculation: $2$ outcomes for $2$ + $2$ outcomes for $3$ = $3$ $4$ outcomes.
Determine Tails and Odd Number Outcomes: Determine the outcomes where the coin shows Tails and the number rolled is odd. The odd numbers on a cube are $1$ , $3$ , and $5$ . Each odd number can pair with Tails. Calculation: $3$ odd numbers $\times 1$ outcome for Tails $= 3$ outcomes.

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