Question

Question No 2: A pair of dice is thrown. Find the probability of getting a total of either 5 or 11.​

Answer 1

Answer:

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Step-by-step explanation:

If a pair of dice is thrown then what is the probability of getting a total of 5 or 11?

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Let X be ours discrete random variable which is the sum of the result of the two dices,them you know that:

P(X=11 or X=5) = P(X=11) + P(X=5) -P(X=11 and X=5)

But the sum of two dices can't be a same time 11 and 5 so P(X=11 and X=5) =0.

Them you know if you try all that the number of all sums possible are 36 = 6*6 and P(X=11) =2/36 = 1 /18 and P(X =5) = 4 /36 = 1/9 ,then:

P(X=11 or X =5) = 1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6

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assumption :X(the result of the dice 1 ) and Y (the result of the dice 2) are independant

Total X+Y=5:

P[X=1,Y=4]=P[X=1]*P[Y=4]=1/6 * 1/6 =1/36

P[X=4,Y=1]=1/6 * 1/6 =1/36

P[X=2,Y=3]=1/6 * 1/6 =1/36

P[X=3,Y=2]=1/6 * 1/6 =1/36

Total X+Y=11:

P[X=5,Y=6]=1/6 * 1/6 =1/36

P[X=6,Y=5]=1/6 * 1/6 =1/36

Thus,

P[X+Y=5 or X+Y=11] = P[X+Y=5 ]+P[ X+Y=11] = 4*1/36 + 2*1/36 =1/6

Hope it helps you !

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