A pair of dice is cast. What is the probability that the sum of the two number landing uppermost is less than 5, if it is known that the sum of the numbers falling uppermost is less than 7?
Combination of 5 = 1,4 - 4,1 - 3,2 or 2,3
Less than seven includes combinations that = 1, 2, 3, 4, 5 or 6.
Calculate the latter combinations and divide the number of those combinations into the former.
7/15
To find the probability that the sum of the two numbers is less than 5, given that the sum is less than 7, we need to determine which outcomes satisfy both conditions.
Let's list all the possible outcomes when two dice are rolled:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (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)
Out of these 36 possible outcomes, only 6 outcomes have a sum less than 7:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1)
Now, let's find the outcomes where the sum is less than 5:
(1, 1), (1, 2), (1, 3), (2, 1)
So, there are 4 outcomes where the sum is less than 5, out of the original 36 possible outcomes.
Therefore, the probability that the sum of the two numbers landing uppermost is less than 5, given that the sum is less than 7, is:
4/36 = 1/9, which can be simplified as approximately 0.1111 or 11.11%.
To find the probability that the sum of the numbers on the pair of dice is less than 5, given that the sum is less than 7, we need to calculate the conditional probability.
Step 1: List all the possible ways the two dice can land, keeping in mind that the sum is less than 7.
The possible outcomes are:
(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)
There are a total of 15 possible outcomes.
Step 2: Identify the outcomes where the sum is less than 5.
The outcomes where the sum is less than 5 are:
(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)
Step 3: Calculate the probability.
The probability is the number of favorable outcomes divided by the total number of possible outcomes.
Number of favorable outcomes = 6
Total number of possible outcomes = 15
Therefore, the probability that the sum of the two numbers landing uppermost is less than 5, given that the sum is less than 7, is 6/15 or 2/5.