a red number cube and a white number cube are rolled. Find the probability that the red number cube shows a 2, given that the sum showing on the two number cubes is less than or equal to 5.

My work: (red cube = [1,2,3,4]
white cube = [4,3,2,1]

Probability of a 2 on the red cube is 1/4. Is this correct?

Block the whole matrix out with read along the top and white down

write all the sums in the boxes of the matrix, which contains 36 numbers.
Of those 36,
4+3+2+1 = 10
have sums less than or equal to 5
Of those 10, 3 show the number 2 on red
w1-r2 , w2-r2 , w3-r2
so 3/10

If the sum is five, then red,white can be

1,4
2,3
3,2
4,1
if the sum is four, then
1,3
2,2
3,1
if the sum is three, then
1,2
2,1
if the sum is two, then
1,1

I see 10 possible combinations, and the red is 2 in 3 of them.

Pr(red=2, sum is =<5) is 3/10

If the sum of the two cubes is 2, 3, 4, or 5 (all the possibilities that are allowed), then the red cube can only be 1, 2, 3 or 4.

The possibile combinations are:
W R
1 4
1 3
1 2
1 1
2 3
2 2
2 1
3 2
3 1
4 1
There are three combinations with a red 2 out of ten allowed. That makes the probability 3/10

LOL - tomorrow we do Blackjack :)

To find the probability that the red number cube shows a 2, given that the sum showing on the two number cubes is less than or equal to 5, you need to determine the favorable outcomes and the total number of outcomes.

Let's first determine the favorable outcomes:
Given that the sum showing on the two number cubes is less than or equal to 5, we need to consider all the combinations that satisfy this condition. The possible combinations are:
(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Out of these combinations, the favorable outcome is (2, 1) because it has a red number cube showing a 2.

Now let's find the total number of outcomes:
Since the red cube has 4 equally likely outcomes (numbers: 1, 2, 3, and 4) and the white cube also has 4 equally likely outcomes (numbers: 1, 2, 3, and 4), the total number of outcomes is 4 * 4 = 16.

Finally, calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
Probability = (number of favorable outcomes) / (total number of outcomes)
= 1 / 16

Therefore, the probability that the red number cube shows a 2, given that the sum showing on the two number cubes is less than or equal to 5, is 1/16.

Your calculation of the individual probability of getting a 2 on the red cube is correct. However, to find the conditional probability, you need to consider the specific condition provided (sum less than or equal to 5) and calculate the probability of the red cube showing a 2 under that condition.