The probability of rolling a die and getting an even number is 1/2. If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) or (1/2)^2. Write an expression to represent the probability of rolling the die (d) times and getting an even number every time. Write the expression to the power of 2.
if getting an even number twice is (1/2)^2
and getting an even number three times is (1/2)^3
then getting an even number d times is (1/2)^d
or
2^-d
Rolling a number less then 4 on a standard number cube
If we represent the probability of rolling a die and getting an even number as p (which is 1/2), then the expression to represent the probability of rolling the die d times and getting an even number every time, raised to the power of 2, can be written as (p^d)^2.
To find the probability of rolling the die (d) times and getting an even number every time, we know that the probability of getting an even number with one roll is 1/2. Therefore, the probability of getting an even number every time when rolling the die d times is (1/2)^d.
To write this expression to the power of 2, we simply square the probability:
((1/2)^d)^2 = (1/2)^(2d)