two regular 6 sided dice are tossed compute the probability of rolling a 3 or doubles
To determine the probability of rolling a 3 or doubles with two regular 6-faced dice, we need to calculate the total number of favorable outcomes and divide it by the total number of possible outcomes:
Total number of possible outcomes when 2 dice are tossed = 6 * 6 = 36 (since each die has 6 faces)
Now we need to count the number of favorable outcomes:
1) Roll a 3: There are two ways to achieve this outcome - (1, 2) and (2, 1).
2) Roll doubles: There are six ways to achieve this outcome - (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
So, the total number of favorable outcomes is 2 + 6 = 8.
Now divide the number of favorable outcomes by the number of possible outcomes:
Probability = Favorable outcomes / Possible outcomes = 8 / 36 = 2 / 9 ≈ 0.222 or 22.2%.
To compute the probability of rolling a 3 or doubles when two regular 6-sided dice are tossed, we first need to determine the number of possible outcomes.
Total number of outcomes when two dice are tossed = 6 x 6 = 36 (each die has 6 sides)
To compute the probability of rolling a 3:
Number of outcomes with a sum of 3 = 2 (1 + 2 and 2 + 1)
Probability of rolling a 3 = Number of favorable outcomes / Total number of outcomes = 2 / 36 = 1/18
To compute the probability of rolling doubles:
Number of outcomes with doubles = 6 (1 + 1, 2 + 2, 3 + 3, 4 + 4, 5 + 5, 6 + 6)
Probability of rolling doubles = Number of favorable outcomes / Total number of outcomes = 6 / 36 = 1/6
Now, since we want to calculate the probability of rolling a 3 or doubles, we add the probabilities together:
Probability of rolling a 3 or doubles = Probability of rolling a 3 + Probability of rolling doubles
= 1/18 + 1/6
= (1 + 3)/18
= 4/18
= 2/9
Therefore, the probability of rolling a 3 or doubles when two regular 6-sided dice are tossed is 2/9.