Question

A non-addictive dice is rolled 1200 times. What is the probability of face 4 occurring between 195 and 210 times, exclusively?

a) 0.15
b) 0.20
c) 0.25
d) 0.30

Answer 1

To find the probability of rolling a face 4 between 195 and 210 times exclusively, we can use the binomial distribution formula. By calculating the probabilities for each number of face 4s and summing them up, we can find the final probability.

Step-by-step explanation:

To find the probability of rolling a face 4 between 195 and 210 times exclusively, we need to calculate the probability of getting exactly 195, 196, 197, ..., 209, or 210 face 4s. Since we have a non-addictive dice, each outcome has an equal probability of 1/6. Therefore, the probability of rolling a face 4 once is 1/6.

Now, we can use the binomial distribution formula to calculate the probabilities for each number of face 4s. The formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials (in this case, 1200), k is the number of face 4s we're interested in (from 195 to 210), and p is the probability of rolling a face 4 once (1/6).

By plugging in the values for each k, summing up all the probabilities, and dividing by the total number of outcomes (6^1200), we can find the final probability.