Question

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?

Answer 1

`P(Even) = 0.547`

Explanation:

Given

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

Required

P(Even)

The even sides are: 2, 4, 6

So:

`P(Even) = P(2) + P(4) + P(6)`

This is then calculated as:

`P(Even) = (n(2))/(Total) + (n(4))/(Total) + (n(6))/(Total)`

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

`P(Even) = (51)/(Total) + (52)/(Total) + (48)/(Total)`

The total frequency is:

`Total =42+51+39+52+44+48`

`Total =276`

So:

`P(Even) = (51)/(Total) + (52)/(Total) + (48)/(Total)`

`P(Even) = (51)/(276) + (52)/(276) + (48)/(276)`

Take LCM

`P(Even) = (51+52+48)/(276)`

`P(Even) = (151)/(276)`

`P(Even) = 0.547` --- approximated