Question

Two dice are rolled find the probability that sum is divisible by 2 and 3

Answer 1

Answer:

ans is 29/36

Step-by-step explanation:

n(s)=36

e=sum of numbers divisible by 2 nd 3

n(e)=29

Answer 2

The probability that sum is divisible by 2 and 3  is $\frac{5}{36}$

Solution:

When two dice are rolled, sample space is given as:

(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)

Therefore,

Total number of possible outcomes = 36

Favorable outcomes = sum is divisible by 2 and 3

Sum should be divisible by both 2 and 3

Favorable outcomes = (1 , 5) , (3 , 3) , (4 , 2) , (5 , 1) , (6 , 6)

Therefore,

Number of favorable outcomes = 5

The probability of an event is given as:

$Probability = \frac{ \text{ number of favorable outcomes }}{ \text{ number of possible outcomes }}\\\\Probability = \frac{5}{36}$

Thus the probability that sum is divisible by 2 and 3  is $\frac{5}{36}$

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