An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled

Question

An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled twice in succession and that the face values of the two goals are added together. This song is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event a: the sun is greater than six

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Thái Dương 2 months 2021-08-02T08:57:13+00:00 1 Answers 3 views 0

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    2021-08-02T08:58:56+00:00

    Answer:

    ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6

    Two dice

    Assuming that the dice are unbiased or not ” loaded”.

    Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.

    How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?

    These are the possibilities

    Case 1.

    D1 =1 & D2=5

    Or

    D1= 5 & D2=1

    Case 2.

    D1 =2 & D2=4

    Or

    D1= 4 & D2= 2

    Case 3. D1=3, D2=3

    P3 =0.027778

    Let’s say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.

    The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.

    P1= 0.02778+ 0.02778 =0.055558

    P2= 0.02778+0.02778 =0.055558

    Same way,

    P3=0.027778, when there is only one way to get the sum 6.

    So, P = 0.138894

    Based on truncating at the sixth decimal place.

    A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.

    Hope This Helps!!!

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