Question

A biased dice is rolled and the results are recorded in a table.

The dice is rolled once more
a) Use the table to estimate the probability that a 3 will be rolled.
b)If the dice is rolled another 500 times, how many sixes would you expect to roll.

Answer 1

a. The estimated probability of rolling a 3 is 11/100 or 0.11.

b. If the biased dice is rolled 500 times, you would expect to roll approximately 60 sixes.

How did we get the values?

a) To estimate the probability of rolling a 3, you can use the formula:

`\[ \text{Probability} = \frac{\text{Frequency of 3}}{\text{Total number of rolls}} \]`

In this case, the frequency of rolling a 3 is 11, and the total number of rolls is the sum of all frequencies:

`\[ \text{Total rolls} = 12 + 35 + 11 + 23 + 7 + 12 \]`

= 100

= 11/100

So, the estimated probability of rolling a 3 is 11/100 or 0.11.

b) To find the expected number of sixes in 500 rolls, you can use the proportion of sixes from the given table and apply it to the total number of rolls. The proportion is:

`\[ \text{Proportion of sixes} = \frac{\text{Frequency of 6}}{\text{Total number of rolls}} \]`

Multiply this proportion by the number of rolls you want to estimate:

`\[ \text{Expected number of sixes} = \text{Proportion of sixes} * \text{Number of rolls (500)} \]`

Expected number of sixes in 500 rolls:

`\[ \text{Proportion of sixes} = (12)/(12 + 35 + 11 + 23 + 7 + 12) \]`

`\[ \text{Expected number of sixes} = (12)/(12 + 35 + 11 + 23 + 7 + 12) * 500 \]`

= 12/100 x 500

= 60

So, if the biased dice is rolled 500 times, you would expect to roll approximately 60 sixes.

Complete question:

A biased dice is rolled and the results are recorded in a table.

The dice is rolled once more

a) Use the table to estimate the probability that a 3 will be rolled.

b)If the dice is rolled another 500 times, how many sixes would you expect to roll.

Score Frequency

1 12

2 35

3 11

4 23

5 7

6 12