You roll 2 dice. The first die has 26 sides and contains the 26 letters of the English alphabet; the other die has 12 sides and contains numbers 1-12. What is the probability that you will roll a letter with one enclosed area (A, D, O, P, Q, R) and a number divisible by 4 (4, 8, 12)?
the two dice are independent events
... the probability of both occurring
... is the product (multiply) of the individual probabilities
p = (6 / 26) * (3 / 12)
remember to reduce fractions where possible
To find the probability of rolling a letter with one enclosed area and a number divisible by 4, we need to determine the total number of possible outcomes and the number of favorable outcomes that meet both conditions.
Total number of outcomes:
The first die has 26 sides with the letters A-Z, and the second die has 12 sides with the numbers 1-12. The total number of possible outcomes is the product of the number of sides on each die, which is 26 x 12 = 312.
Favorable outcomes:
We need to calculate the number of outcomes that meet both conditions, which is a letter with one enclosed area (A, D, O, P, Q, R) and a number divisible by 4 (4, 8, 12).
There are 6 letters with one enclosed area (A, D, O, P, Q, R) out of the 26 possible letters.
There are 3 numbers divisible by 4 (4, 8, 12) out of the 12 possible numbers.
To find the number of favorable outcomes, we multiply the number of options for each condition: 6 x 3 = 18.
Probability:
Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
P(A) = favorable outcomes / total outcomes
P(A) = 18 / 312
Therefore, the probability of rolling a letter with one enclosed area and a number divisible by 4 is 18/312, which can be simplified as 3/52.