If the first dice yields an even number, what is the probability that the sum of the two dices will be equal to 12?
1st Die
P(even) = 3/6 = 0.50
P(6|even) = 1/3 = 0.333
2nd Die
P(6) = 1/6 = .1667
So P(12) = 0.33*0.1667 ?
To find the probability that the sum of the two dice will be equal to 12, given that the first dice yields an even number, you need to use conditional probability.
First, you correctly calculate the probability of the first dice yielding an even number as 3/6 or 0.50.
Next, you calculate the probability of getting a 6 on the second dice, which is 1/6 or approximately 0.1667.
To find the probability that the sum of the two dice will be 12, given that the first dice is even, you multiply the probability of the first dice being even (0.50) by the probability of getting a 6 on the second dice (0.1667):
P(12|even) = P(even) * P(6) = 0.50 * 0.1667 = 0.08335
So, the probability is approximately 0.08335 or 8.33%.