When two dice are thrown simultaneously What is the probability that the sum of the two is an odd number?

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by :

Let ‘x’ be the number on the first dice

‘Y’ be the number on second dice

First dice showing odd number = {1,3,5}

Second dice also has odd number = {1,3,5}

The probability that the first dice shows an odd number = 3/6.

The probability that the second dice shows an odd number = 3/6.

The possible results are (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5).

The probability that both dice show an odd number is (3/6) × (3/6)

= 9/36

= 1/4

Therefore, the probability of getting an odd number in both dice is 1/4.

Summary:

If you roll two fair six-sided dice, the probability that both dice show an odd number is 1/4.

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To answer the question: 5/11 and 6/11.

The possible sum of rolling two dice is 2,3,4.....,12. Total 11 possibilities, 5 odds and 6 evens. Now, the probability of each sum value is not alike for all possibilities. For eg., sum 2 - (1,1) - prob: 1/36 Sum 3 - (1,2),(2,1) - prob: 2/36 . . Sum 10- (5,5),(4,6),(6,4) prob:3/36 Sum 12-(6,6) prob:1/36 Hence, had it been the sum probabilities are same then 5/11 and 6/11 are valid. But since the probabilities are different, actual probabilities of odds is 18/36 or 1/2.