Question

App 19.study

Tools
Tools
Probability
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results.
Complete the table below.
0.232
37
24
0.176
18
0.048
0.104
22
Result of Roll
Frequency
Experimental
Probability
1
2
13
3
0.144
4
29
5
0.296
6
Reset
Submit

Answer 1

`1 \to 22 \to 0.176`

`2 \to 13 \to 0.104`

`3 \to 18 \to 0.144`

`4 \to 29 \to 0.232`

`5 \to 37 \to 0.296`

`6 \to 6 \to 0.048`

Explanation:

Given

`n = 125`

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

`Pr = (Frequency)/(n)`

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

`Pr(2) = (13)/(125) = 0.104`

`Pr(4) = (29)/(125) = 0.232`

`Pr(6) = (6)/(125) = 0.048`

When the frequency is to be calculated, we use:

`Pr = (Frequency)/(n)`

`Frequency = n * Pr`

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

`Frequency(3) = 125 * 0.144 = 18`

`Frequency(5) = 125 * 0.296 = 37`

For roll of 1 where the frequency and the probability are not known, we use:

`Total \ Frequency = 125`

So:

Frequency(1) added to others must equal 125

This gives:

`Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125`

`Frequency(1) + 103 = 125`

Collect like terms

`Frequency(1) =- 103 + 125`

`Frequency(1) =22`

The probability is then calculated as:

`Pr(1) = (22)/(125)`

`Pr(1) = 0.176`

So, the complete table is:

`1 \to 22 \to 0.176`

`2 \to 13 \to 0.104`

`3 \to 18 \to 0.144`

`4 \to 29 \to 0.232`

`5 \to 37 \to 0.296`

`6 \to 6 \to 0.048`