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Euriana Covilhă
Can I create a Tree Diagram?
Time:
9:56
Submit Assessment
Padraic is playing a game with his friend, Radnor. Padraic rolls a 4 sided die twice. If Padraic rolls at least a 3 on either roll, then Radnor gives him 1 gobstopper, otherwise, Padraic has to give Radnor 1 gobstopper.
Let's give the label
A to the event that Padraic rolls at least a
3 on either roll. What is the probability of this event?
14

5//16
answered
Flag for later
Previous
6 of 16
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Euriana Covilhă $\newline$ Can I create a Tree Diagram? $\newline$ Time: $\newline$ $9$ : $56$ $\newline$ Submit Assessment $\newline$ Padraic is playing a game with his friend, Radnor. Padraic rolls a $4$ sided die twice. If Padraic rolls at least a $3$ on either roll, then Radnor gives him $1$ gobstopper, otherwise, Padraic has to give Radnor $1$ gobstopper. $\newline$ Let's give the label $\mathrm{A}$ to the event that Padraic rolls at least a $\mathbf{3}$ on either roll. What is the probability of this event? $\newline$ $14$ $\newline$ $5 / 16$ $\newline$ answered $\newline$ Flag for later $\newline$ Previous $\newline$ $6$ of $16$ $\newline$ Next

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Find probabilities using the binomial distribution

Full solution

Q. Euriana Covilhă

\newline

Can I create a Tree Diagram?

\newline

Time:

\newline

9

:

56

\newline

Submit Assessment

\newline

Padraic is playing a game with his friend, Radnor. Padraic rolls a

4

sided die twice. If Padraic rolls at least a

3

on either roll, then Radnor gives him

1

gobstopper, otherwise, Padraic has to give Radnor

1

gobstopper.

\newline

Let's give the label

\mathrm{A}

to the event that Padraic rolls at least a

\mathbf{3}

on either roll. What is the probability of this event?

\newline

14

\newline

5 / 16

\newline

answered

\newline

Flag for later

\newline

Previous

\newline

6

of

16

\newline

Next

Calculate Probability: First, let's figure out the probability of rolling at least a $3$ on a $4$ -sided die in one roll. There are two outcomes that work: rolling a $3$ or a $4$ . So the probability for one roll is $2$ out of $4$ , or $\frac{1}{2}$ .
Consider Two Rolls: Now, we need to consider two rolls. To find the probability of event $A$ (rolling at least a $3$ on either roll), we can first find the probability of the opposite event (not rolling at least a $3$ on both rolls) and then subtract it from $1$ .
Calculate Probability for Two Rolls: The probability of not rolling at least a $3$ (so rolling a $1$ or $2$ ) on one roll is $2$ out of $4$ , or $\frac{1}{2}$ . For two rolls, we multiply the probabilities: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ .
Subtract from $1$ : Subtract the probability of not rolling at least a $3$ on both rolls from $1$ to get the probability of event $A$ : $1 - \frac{1}{4} = \frac{3}{4}$ .
Correct Mistake: However, I made a mistake in the previous step. The probability of not rolling at least a $3$ on one roll is actually $\frac{1}{2}$ , but for two rolls, it should be $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ . This is correct, but I need to convert $\frac{3}{4}$ to a fraction with a denominator of $16$ to match the answer choices. $\frac{3}{4}$ is equivalent to $\frac{12}{16}$ .

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