# Question Video: Using Experimental Probability to Determine the Expected Number of Outcomes of an Event Mathematics • 7th Grade

The table shows the results of rolling a die 78 times. Using this information, how many times is the number 2 expected to appear if the die is rolled 234 times?

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### Video Transcript

The table shows the results of rolling a die 78 times. Using this information, how many times is the number two expected to appear if the die is rolled 234 times?

The table tells us that the number one was rolled 23 times. Number two was rolled 17 times. There were 15 threes, 10 fours, two fives, and 11 sixes rolled. We are also told that the die was rolled a total of 78 times. This can be checked by adding 23, 17, 15, 10, two, and 11.

We are asked to find the expected number of times the number two would be rolled if the die was rolled 234 times. We recall that the expected value can be calculated by multiplying the probability of an event occurring by the number of trials or experiments. Before we can apply this formula, we need to calculate the experimental probability of rolling a two. The experimental probability of rolling a two with this die is equal to the number of twos in the table over the total number of rolls in the table, which is 17 over 78, since there were 17 twos rolled and the die was rolled a total of 78 times.

To work out the expected number of twos from 234 rolls, we now apply the expected value formula. We need to multiply the expected probability by the number of rolls. We therefore need to multiply 17 over 78 by 234. 78 and 234 are both divisible by 78, so we can simplify this calculation as shown. Finally, multiplying 17 by three gives us 51.

We can therefore conclude that using the information in the table, we would expect the number two to appear 51 times if the die was rolled a total of 234 times.