### Video Transcript

The probability that a biased die
will land on an even number is 0.6. If the die is rolled 80 times, how
many times is it expected to land on an even number?

We’re told that this die is
biased. So instead of the usual probability
of landing on an even number of 0.5, the probability is instead 0.6. The die is going to be rolled 80
times. And we’re asked how many times the
die is expected to land on an even number.

We can recall the formula for
calculating the expected value or expected frequency of a particular event. It’s equal to the probability of
that event occurring multiplied by the number of trials that are performed. In the context of this question,
the expected number of times that the die will land on an even number is equal to
the probability of the die landing on an even number in a single roll multiplied by
the number of times we roll the die. Both of these values are given in
the question. So the expected value is 0.6
multiplied by 80, which is 48. If we roll this biased die 80
times, we would expect it to land on an even number 48 times.

It’s important to remember that
what actually happens will likely be different. The die may land on evens 47 or 49
times or even a number further away. But if we had to choose the most
likely outcome, it would be that the die landed on an even number 48 times.