Two dice are thrown simultaneously find the probability of getting an odd number as the sum

Two dice are thrown simultaneously. The probability of getting the sum equal to an odd number is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Given:

Two dice are thrown.

Formula Used:

Probability = Number of observation/Total number of observation

Calculation:

The odd sum is 3 , 5, 7, 9, 11

The number of ways getting 3 = (1, 2), (2, 1) = 2

The number of ways getting 5 = (1, 4), (2, 3), (3, 2), (4, 1) = 4

The number of ways getting 7 = (1, 6), (2, 5), (3, 4),(4, 3), (5, 2), (6, 1) = 6

The number of ways getting 9 = (3, 6), (4, 5), (5, 4), (6, 3) = 4

The number of ways getting 11 = (5, 6), (6, 5) = 2

The number of ways = 2 + 4 + 6 + 4 + 2 = 18

The total number of ways = 6 × 6 = 36

Probability = 18/36 = 1/2

∴ The probability of getting an odd sum is 1/2.