Question

A biased dice is thrown.
The probability of each score is shown:
1 = 0.15
2 = 0.08
3 = 0.3
4 = 0.05
5 = 0.22
6 = 0.2

The dice is thrown 200 times.
How many times should we expect the score to be even

Answer 1

wrong

Answer 2

To calculate the expected number of times the score is even, we need to find the probability of getting an even score for each possible outcome and multiply it by the number of throws (200).

The even scores are 2, 4, and 6.
The probability of getting a 2 is 0.08, so we expect to get a 2 (2 * 0.08 * 200) = 32 times.
The probability of getting a 4 is 0.05, so we expect to get a 4 (0.05 * 200) = 10 times.
The probability of getting a 6 is 0.2, so we expect to get a 6 (0.2 * 200) = 40 times.

Adding these together, we should expect the score to be even (32 + 10 + 40) = 82 times.

Answer 3

Apologies for the mistake.

To find the expected number of times the score is even, we need to sum the probabilities of getting even scores (2, 4, or 6) and then multiply by the total number of throws (200).

The probability of getting a 2, 4, or 6 is 0.08 + 0.05 + 0.2 = 0.33.

Now, we can find the expected number of times by multiplying the probability by the total number of throws: 0.33 * 200 = 66.

Thus, we should expect the score to be even approximately 66 times.