Emma will roll two number cubes labeled 1 through 6. She will record the sum of the two numbers after each roll. She will roll the two cubes 540 times. How many times should Emma expect the sum to equal 5?
Out of the 36 possibilities, 5 can be obtained by 1,4 or 4,1 or 2,3 or 3,2. That is probability of 4/36 = 1/9. What is 1/9 of 540?
To find the number of times Emma should expect the sum to equal 5, we need to calculate the probability of rolling a sum of 5 on two number cubes.
The possible combinations to get a sum of 5 are (1,4), (2,3), (3,2), and (4,1). There are four different combinations for a sum of 5.
Since each cube has 6 sides and there are two cubes, the total number of possible outcomes is 6 * 6 = 36.
To find the probability of rolling a sum of 5, we divide the number of favorable outcomes (4) by the total number of possible outcomes (36):
Probability = 4/36 = 1/9
Since Emma will roll the two cubes 540 times, we can multiply the probability by the number of rolls to find the expected number of times she should get a sum of 5:
Expected number of times = Probability * Number of rolls
Expected number of times = (1/9) * 540
Expected number of times = 60
Therefore, Emma should expect to get a sum of 5 approximately 60 times.
To determine how many times Emma should expect the sum to equal 5, we need to calculate the probability of rolling a sum of 5 for each roll and then multiply it by the total number of rolls.
To find the probability of rolling a sum of 5, we consider the number of ways the dice can add up to 5 and divide it by the total number of possible outcomes.
The possible sums that add up to 5 are:
- (1, 4)
- (4, 1)
- (2, 3)
- (3, 2)
So, there are 4 possible ways to get a sum of 5.
Since each cube has 6 sides, the total number of possible outcomes for a single roll is 6 x 6 = 36.
Therefore, the probability of rolling a sum of 5 in a single roll is 4/36, which simplifies to 1/9.
To calculate the expected number of times Emma should roll a sum of 5 in 540 rolls, we multiply the probability of rolling a sum of 5 (1/9) by the total number of rolls (540):
Expected number = Probability x Total number of rolls
Expected number = (1/9) x 540
Expected number = 60
Therefore, Emma should expect to roll a sum of 5 around 60 times out of 540 rolls.