A pair of dice is rolled. Let G be the event that the sum will be an even number and H be the event that the sum will be greater than 6. Find GuH
G U H = sum will be 2,4,6,7,8,9,10,11,12
To find the probability of the event G u H (G union H), we need to calculate the probability that the sum of the two dice is either an even number or a number greater than 6.
Let's consider the possible outcomes when rolling two dice:
For the sum to be an even number, we need one of the following combinations:
(1, 1), (1, 3), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (3, 6), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (5, 6), (6, 1), (6, 2), (6, 4), (6, 6).
There are a total of 36 possible outcomes (6 numbers on one die multiplied by 6 numbers on the other die).
For the sum to be greater than 6, we need one of the following combinations:
(1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
Out of these 36 possible outcomes, 21 of them have a sum greater than 6.
To find the probability of G u H, we need to count the outcomes that satisfy either G or H (or both) and divide it by the total possible outcomes.
From the above combinations, the outcomes that satisfy either G or H (or both) are:
(1, 1), (1, 3), (1, 5), (1, 6), (2, 2), (2, 4), (2, 5), (2, 6), (3, 1), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
So there are 29 outcomes that satisfy either G or H (or both).
The probability of G u H is given by:
P(G u H) = (Number of outcomes that satisfy either G or H) / (Total possible outcomes)
P(G u H) = 29 / 36
Therefore, the probability of the event G u H is 29/36.