Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both dice is 5.
For either-or probabilities, add the individual probabilities. P(5) = 1/6
Sum of 5 can be obtained by (1,4)(4,1)(2,3)(3,2)
P(1,4) = 1/6 * 1/6 = ?
P(4,1) = ?
P(3,2) = 1/6 * 1/6 = ?
P(2,3) = ?
To find the probability of getting a 5 on either die or the sum of both dice is 5, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
The total number of possible outcomes when rolling two dice is given by the product of the number of possible outcomes on each die. Since each die has 6 sides, the total number of possible outcomes is 6 × 6 = 36.
Now let's determine the favorable outcomes:
1. Getting a 5 on either die: There are two scenarios where this can happen: either the first die shows a 5 and the second die can be any number (6 possibilities), or the first die can be any number (6 possibilities) and the second die shows a 5. Thus, the number of favorable outcomes for this scenario is 6 + 6 = 12.
2. The sum of both dice being 5: There are four possible combinations of numbers that can give a sum of 5: (1, 4), (2, 3), (3, 2), and (4, 1). So, the number of favorable outcomes for this scenario is 4.
Now we can sum up the number of favorable outcomes for both scenarios: 12 + 4 = 16.
Therefore, the probability of getting a 5 on either die or the sum of both dice is 5 is given by the favorable outcomes divided by the total outcomes:
P(5 on either die or sum of 5) = favorable outcomes / total outcomes
= 16 / 36
= 4 / 9
So, the probability is 4/9.