Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 10)
10.
Two dice are tossed. The probability that the total score is a prime number is:
1
6
5
12
1
2
7
9
Answer: Option
Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

Then E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
      (5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

P(E) = n(E) = 15 = 5 .
n(S) 36 12

Discussion:
64 comments Page 1 of 7.

Deepak said:   1 month ago
We get the number from the first dice = 1,2,3,4,5,6
And the same from the second dice.
We have prime numbers in both dice is 1, 2, 3, 4, 5 and a total of 1+2=3 is a prime number.
So, total 12.

We have 5 prime numbers and a total score number.
So, 5/12 is the answer.

Bini said:   2 years ago
The possible outcomes for the sum of two dice are as follows:

Sum: 2
Possible outcomes: (1, 1).

Sum: 3
Possible outcomes: (1, 2), (2, 1).

Sum: 5
Possible outcomes: (1, 4), (2, 3), (3, 2), (4,1).

Sum: 7
Possible outcomes: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).

Sum: 11
Possible outcomes: (5, 6), (6, 5).

So, there are 15 possible outcomes.
(3)

Riuhsi said:   3 years ago
2 is the prime number @Sabin Banset.
(2)

Sabin Basnet said:   3 years ago
When we add 1 and 1 it becomes 2.
So, 2 is not a prime number.
So, there is n(e) = 14 only
And 14/36 = 7/18.
That's all.
(3)

Maths said:   3 years ago
1 is not a prime number.

So, the correct answer is 14/36 = 7/18.

Trisha said:   5 years ago
@Rutvik.

There (1,1) consider only once because there is no difference between 1, 1 or 1, 1, but there is always a difference between 2, 5 or 5, 2.

Suppose dice 1 and dice 2 have the same no. Like (1, 1) how will you differentiate dice 1 and 2 but if the no. Are change like (1, 2) (2, 1) or (5, 2) (2, 5) you will differentiate dice 1 and 2. That's why.

I hope now you will understand.

Anu said:   5 years ago
@Sowmya.

Yes, the total score here means the sum of numbers.

Priya said:   5 years ago
@All.

Why here we perform addition operation to get a Prime number? Instead of getting total as prime we use (product or subtract).

Why only addition is performed? Can anybody explain this clearly!

Ruthvik Gowda said:   5 years ago
Why (1, 1) conisdered only once ?

Since there is two dices we can get (1, 1) twice right, like this combination (2, 5) & (5, 2).
(2)

Sweta said:   5 years ago
Are 4 and 6 prime numbers?

4 and 6 divisible by not only 1 and itself, but it is also divisible by 2, 3.


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