John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
Answer: A number cube has 3 even numbers. Each even number has a theoretical probability of 1/6. In 60 rolls, an even number could come up ten times. Since there are 3 even numbers, the total predicted value is 30. So 20 is a low prediction.
A number cube has 3 even numbers. Each even number has a theoretical probability of 1/6. In 60 rolls, an even number could come up ten times. Since there are 3 even numbers, the total predicted value is 30. So 20 is a low prediction.
thank you
To determine if John's prediction of 20 times landing on an even number is a good prediction, we need to compare it with the theoretical probability.
Theoretical probability refers to the likelihood of an event occurring based on mathematical principles. In this case, we will calculate the probability of rolling an even number on a fair six-sided number cube.
A fair number cube has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Out of these six possibilities, three are even numbers (2, 4, and 6).
To find the probability of rolling an even number, we divide the number of desired outcomes (3) by the total number of possible outcomes (6):
P(rolling an even number) = 3/6 = 1/2
This means the probability of rolling an even number is 1/2 or 0.5, also expressed as 50%.
Now, let's calculate the predicted number of times the cube will land on an even number based on theoretical probability:
Number of times the cube will land on an even number = Theoretical Probability * Total number of rolls
Prediction = 0.5 * 60 = 30
According to theoretical probability, the predicted number of times the cube will land on an even number is 30.
Comparing this to John's prediction of 20 times, we can see that his prediction is lower than the theoretical prediction. This means his prediction is below the expected value based on theoretical probability. Therefore, we could say that John's prediction is not a good prediction based on theoretical probability.
half of the numbers on the cube are even
so a fair cube should have half of the outcomes even