A number cube is labelled 1 to 6. The cube is rolled 60 times. Predict how many times each outcome will occur. Explain each answer.
a)1 is rolled.
b)An even number is rolled
c)A number greater than 3 is rolled
d)9 is rolled.
You don't have to answer every question. Just answer one but tell me how you did it.
a fair cube is expected to come up an equal number of times on each side
6 sides, 60 rolls
... each side is expected 10 times
a) 10 ... expected outcome
b) 30 ... expected outcome
c) 30 ... expected outcome
d) 0 ... only 6 sides
Let's tackle the first question: How many times will 1 be rolled when a number cube is rolled 60 times?
To answer this question, we need to consider the probability of rolling a 1. The number cube has six sides, and only one of them is labeled with a 1. Therefore, the probability of rolling a 1 on a single roll is 1/6.
To find out how many times a 1 is likely to occur out of 60 rolls, we multiply the probability of rolling a 1 by the number of rolls:
(1/6) * 60 = 10.
Therefore, we can predict that 1 will be rolled about 10 times in 60 rolls.
Explanation: By calculating the probability of the desired outcome for a single event and then multiplying it by the number of trials, we can predict the expected number of occurrences. In this case, the probability of rolling a 1 (1 out of 6) is multiplied by the total number of rolls (60) to get the expected number of occurrences of 1 in 60 rolls.
Okay, let's start with the first question: "How many times will 1 be rolled?"
To answer this, we need to know that the number cube has 6 faces, labeled from 1 to 6. Since each face has an equal probability of landing face up when rolled, we can assume that the probability of rolling a specific number is 1/6.
Now, we know that the cube is rolled 60 times. Therefore, we can calculate the expected number of times we would roll a 1 by multiplying the probability of rolling a 1 by the total number of rolls.
Expected number of times rolling a 1 = Probability of rolling a 1 * Total number of rolls
Expected number of times rolling a 1 = (1/6) * 60
Expected number of times rolling a 1 = 10
So, we can predict that 1 will be rolled approximately 10 times.
Please let me know if there's anything else I can help with!