a) Predict the number of 6s you will get if you roll a number cube 30 times.
b) Predict the number of even numbers you will get if you roll a number cube 25 times.
a) there are 6 faces on the cube
... a 6 (or any other specific number) is expected 1/6 of the time
... 1/6 * 30 = ?
b) half of the numbers on the cube are even
... half of the rolls are expected to result in even numbers
Predict no of 6s
To predict the number of specific outcomes when rolling a fair number cube, we need to consider the probability of that outcome occurring and multiply it by the number of trials.
a) Predicting the number of 6s when rolling a number cube 30 times:
1. Find the probability of rolling a 6 on a fair number cube: A standard number cube has 6 faces, and each face has an equal chance of landing face-up. So the probability of rolling a 6 is 1/6.
2. Multiply the probability by the number of trials: 1/6 * 30 = 5.
Therefore, it is predicted that you will get approximately 5 6s if you roll a number cube 30 times.
b) Predicting the number of even numbers when rolling a number cube 25 times:
1. Determine the probability of rolling an even number on a fair number cube: Half of the faces on a number cube are even numbers (2, 4, 6), and the other half are odd numbers (1, 3, 5). So the probability of rolling an even number is 3/6 = 1/2.
2. Multiply the probability by the number of trials: 1/2 * 25 = 12.5.
Since we cannot have half a roll, we need to round the result to the nearest whole number. Therefore, it is predicted that you will get approximately 13 even numbers if you roll a number cube 25 times.
well,
P(6) = 1/6
P(even) = 3/6
so now multiply each probability by the number of rolls.