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A standard six-sided die was rolled a number of times, and the results were recorded in the table below. Use this information to answer the question. Type your answer into the box as a decimal, rounded to the nearest thousandth.

Side: 1 2 3 4 5 6
Frequency: 42 51 39 52 44 48


What is the probability that an even number was rolled?

Respuesta :

MrRoyal

Answer:

[tex]P(Even) = 0.547[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccccc}{Sides} & {1} & {2} & {3} & {4} & {5} & {6} \ \\ {Freq} & {42} & {51} & {39} & {52} & {44} & {48} \ \end{array}[/tex]

Required

P(Even)

The even sides are: 2, 4, 6

So:

[tex]P(Even) = P(2) + P(4) + P(6)[/tex]

This is then calculated as:

[tex]P(Even) = \frac{n(2)}{Total} + \frac{n(4)}{Total} + \frac{n(6)}{Total}[/tex]

Replace n(2), n(4), n(6) with their frequencies

[tex]P(Even) = \frac{51}{Total} + \frac{52}{Total} + \frac{48}{Total}[/tex]

The total frequency is:

[tex]Total =42+51+39+52+44+48[/tex]

[tex]Total =276[/tex]

So:

[tex]P(Even) = \frac{51}{Total} + \frac{52}{Total} + \frac{48}{Total}[/tex]

[tex]P(Even) = \frac{51}{276} + \frac{52}{276} + \frac{48}{276}[/tex]

Take LCM

[tex]P(Even) = \frac{51+52+48}{276}[/tex]

[tex]P(Even) = \frac{151}{276}[/tex]

[tex]P(Even) = 0.547[/tex] --- approximated

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