Question

Probability of getting the sum as 4 when a pair of dice is rolled​

Answer 1

Answer:

There are six faces for each of two dice, giving 36 possible outcomes. If the two dice are fair, each of 36 outcomes is equally likely.

Three outcomes sum to 4: (1+3), (2+2) and (3+1).

Probability of getting a sum of 4 on one toss of two dice is 3/36, or 1/12.

Answer 2

Probability of getting the sum as 4 when a pair of dice is rolled is 1/12

Given :

A pair of dice is rolled

To find :

The probability of getting a sum of 4

Solution :

Step 1 of 3 :

Find total number of possible outcomes

Here it is given that a pair of dice is rolled

So the event points are

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

So the total number of possible outcomes = 36

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that of getting a sum of 4

So the event points are (1,3) , (2,2) , (3,1)

So total number of possible outcomes for the event A is 3

Step 3 of 3 :

Find the probability

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{3}{36} }$

$\displaystyle \sf{ = \frac{1}{12} }$

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