Question

1- Two different dice are rolled together. Find the probability of getting
() the sum of numbers on two dice to be 4
(ii) even number on both the dice
​

Answer 1

Step-by-step explanation:

If two different dice are rolled together what is the probability of getting an even number on both dice?

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If the dice is six sided, only 50% of the first dice fulfill the requirement of being even (2,4,6). If the other dice only needs to be even (not identical to the first) we need one of the three even numers to pop up on the second dice from the six available ones. So here again the chances are 3/6 or 1/2. So just getting two even dice (not necessarily equal), has a 1/2 ×1/2 = 1/4 (25%) chance.

Lets answer the question slightly differently now. What about two identical even numbers?

Now what if the second dice needs to be identical to the first (which was even), making it only a 1 in 6 or 1/6 chan

Don’t let change and uncertainty hold you back.

If we consider the dice to be six-sided labelled as 1,2,3,4,5,6. Then the required event is the occurrence of number (2,4&6).

It is not given that each number is equally probable, then let the probability for 1,2,3,4,5,6 on dice 1 and dice 2 be p1, p2, p3, p4, p5, p6 and q1, q2, q3, q4, q5, q6 respectively.

Now, the probability of getting an even number on dice 1, e1= p2+p4+p6

Similarly for dice 2,e2= q2+q4+q6

Hence, for the occurrence of both the event=

e1*e2= (p2+p4+p6)*(q2+q4+q6)

And, for the assumption that all the numbers on both the dices are equally probable,then, required probability = (3/6)*(3/6)= 1/4

Answer 2

NUMBER OF DICE ROLLED = 2

NUMBER OF OUTCOMES = 12

(i) P(OF GETTING SUM OF NUMBERS TO BE 4) = 2/12 = 1/6

(ii) P (OF GETTING AN EVEN NUMBER) = 6/12 = 1/2

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