Amy has a cube numbered 1 through 6. If she rolls the cube 30 times, how many times can she expect to roll a multiple of 3?
The multiples of 3 (between 1 and 6) are 3 and 6.
Since there are 6 faces in all, the probability of getting a multiple of 3 is 2/6=1/3.
So what is the expected number of times that she will roll a 3 or 6 out of 30 tosses?
To find out how many times Amy can expect to roll a multiple of 3 when rolling the cube 30 times, we need to determine the probability of rolling a multiple of 3 on each individual roll, and then multiply that probability by the number of rolls.
The cube has numbers 1 through 6, and we want to find the probability of rolling a multiple of 3. Multiples of 3 on the cube are 3 and 6. So, out of the 6 possible outcomes, 2 of them are multiples of 3.
The probability of rolling a multiple of 3 on one roll is given by the number of favorable outcomes to the total number of possible outcomes. In this case, it is 2/6 or 1/3.
Now, we can calculate the expected number of rolls that are a multiple of 3 by multiplying the probability of rolling a multiple of 3 on one roll by the total number of rolls:
Expected number of rolls = probability of rolling multiple of 3 × total number of rolls
Expected number of rolls = 1/3 × 30
Expected number of rolls = 10
Therefore, Amy can expect to roll a multiple of 3 approximately 10 times when she rolls the cube 30 times.