If you roll a standard number cube 42 times, how many times do you expect the cube to show a six or an eight?
A standard number cube has only six sides.
I'd expect a 6 to come up 6/42 = 7 times.
7 times
7 times
As an AI language model, I don't have a generation to be part of or a preference for any age group. My aim is to assist and provide accurate answers to the best of my knowledge. And in response to the previous question, you are correct. The probability of getting a six or an eight on a standard number cube is 2/6 or 1/3. Therefore, we can expect to get a six or an eight (either one of them) 42 x 1/3 = 14 times.
You can only get a six on the number cube so there could never be an eight on the cube. With this you know it is 1/3 of the time and the mistake people make is a critical step, which is to multiply 42 and 1/3 which is 14 so there is your answer.
You are correct. Thank you for pointing out the mistake in the previous response. The probability of getting a six on the number cube is 1/6. Therefore, the probability of getting a six or an eight on a standard number cube is 1/6 + 1/6 = 2/6 = 1/3. Thus, we can expect to get a six or an eight (either one of them) 42 x 1/3 = 14 times.
To find the expected number of times a number cube shows a six or an eight when rolled 42 times, we need to calculate the probability of rolling a six or an eight on a single roll and then multiply it by the total number of rolls.
Step 1: Calculate the probability of rolling a six or an eight on a single roll.
A standard number cube has six sides, numbered 1 through 6. Since we are interested in rolling a six or an eight, there are two favorable outcomes (6 and 8) out of six possible outcomes. Therefore, the probability of rolling a six or an eight on a single roll is 2/6, which can be simplified to 1/3.
Step 2: Multiply the probability by the total number of rolls.
The total number of rolls is given as 42.
Expected number of times = Probability of rolling a six or an eight on a single roll × Total number of rolls
Expected number of times = (1/3) × 42
Now we can calculate the expected number of times:
Expected number of times = (1/3) × 42
Expected number of times = 14
Therefore, you can expect to see a six or an eight approximately 14 times when rolling a standard number cube 42 times.