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Please could someone help with the below statistics question please? Watch

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    The discrete random variable x represents the score on the uppermost face of a biased die with six faces. The probability distribution of X is shown in the table below.
    x 1 2 3 4 5 6
    P(X= x) 0.1 0.1 0.1 0.2 0.2 0.3

    The discrete random variable y represents the score on the uppermost face of a biased die with five faces. The probability distribution of Y is shown in the table below.

    y 1 2 3 4 5
    P(Y= y) 0.1 0.1 0.4 0.2 0.2

    Each die is rolled once. The scores on the two dice are independent.
    Find the probability that the sum of the two scores equals 2.

    Please could someone explain to me why the answer is:
    P(X=1)P(Y=1) = 0.1 x 0.1 = 0.01

    and not P(X=1)P(Y=1) = 0.1 x 0.1 OR P(Y=1)P(X=1) = (0.1x0.1) + (0.1x0.1) = 0.02.

    I don't understand why you don't account for the possibility that you choose the other die first.
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    It might help to think about this in terms of a tree. Let's say the first tier of the tree represents the die with six faces. This first tier will have six branches, and for each of those there will be five sub-branches to represent the die with five faces. You could take the dice in the opposite order - it makes no difference, you will end up with 30 sub-branches either way. Only one of the 30 sub-branches corresponds to a score of 1 on both dice. Order doesn't come into it - there is only one way to score two in total.

    Where you would need to think about order is if you were looking at the probability of a total score of (say) 3. There would be two ways to do that: 2 on the 6-die and 1 on the 5-die or 1 on the 6-die and 2 on the 5-die. Then you would need to add the probabilities of scoring 2+1 and 1+2 (and those two outcomes would be represented by two separate sub-branches of the tree mentioned above).
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    Thanks so much - that's a really helpful explanation!

    (Original post by old_engineer)
    It might help to think about this in terms of a tree. Let's say the first tier of the tree represents the die with six faces. This first tier will have six branches, and for each of those there will be five sub-branches to represent the die with five faces. You could take the dice in the opposite order - it makes no difference, you will end up with 30 sub-branches either way. Only one of the 30 sub-branches corresponds to a score of 1 on both dice. Order doesn't come into it - there is only one way to score two in total.

    Where you would need to think about order is if you were looking at the probability of a total score of (say) 3. There would be two ways to do that: 2 on the 6-die and 1 on the 5-die or 1 on the 6-die and 2 on the 5-die. Then you would need to add the probabilities of scoring 2+1 and 1+2 (and those two outcomes would be represented by two separate sub-branches of the tree mentioned above).
 
 
 
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