Part A:
To determine how many times we would expect the result to be an even number greater than 2, we need to calculate the probability of rolling an even number greater than 2 on a number cube.
There are three even numbers greater than 2 on a number cube, which are 4, 5, and 6. Out of the six possible outcomes (numbers 1 through 6), half of them are even numbers greater than 2.
Therefore, the probability of rolling an even number greater than 2 is 1/2.
To find the expected number of times, we multiply the probability by the total number of rolls:
Expected number of times = Probability * Total number of rolls
Expected number of times = (1/2) * 180
Expected number of times = 90
Therefore, we would expect the result to be an even number greater than 2 approximately 90 times.
Part B:
To determine how many times we would expect the result to be a number less than 6, we need to calculate the probability of rolling a number less than 6 on a number cube.
There are five numbers less than 6 on a number cube, which are 1, 2, 3, 4, and 5. Out of the six possible outcomes (numbers 1 through 6), five of them are less than 6.
Therefore, the probability of rolling a number less than 6 is 5/6.
To find the expected number of times, we multiply the probability by the total number of rolls:
Expected number of times = Probability * Total number of rolls
Expected number of times = (5/6) * 180
Expected number of times = 150
Therefore, we would expect the result to be a number less than 6 approximately 150 times.