Question

Find the probability of getting the sum of the numbers as 8 when two dice are thrown simultaneously.​

Answer 1

$\sf \: Solution:$

Let us write the possible outcomes on rolling two dice simultaneously and then highlight the outcomes where the sum of the numbers on the dice is 8.

(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)

Thus, total number of outcomes of throwing two dice simultaneously = 36

Let the event of getting the sum of the numbers on the dice as 8 be E.

The outcomes where the sum of the numbers is 8 are: (6, 2) (5, 3), (4, 4) (4, 4), (3, 5) , (2, 6)

Therefore Number of favourable outcomes for occurrence of event E = 5

So, probability of getting the sum as 8

$\sf= \frac{Number \: of \: favourable \: outcomes}{ Total \: number \: of \: possible \: outcomes }= \frac{5}{36}$

$\sf \: Therefore, \: probability \: of \: getting \: the \: sum \: of \: numbers \\ \sf as \: 8 \: when \: two \: dice \: are \: thrown \: simultaneously \: is \: \frac{5}{36}$

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More information :-

• An experiment with unpredictable outcomes is called a random experiment.
• One or more outcomes of an experiment form an event.
• The outcomes of an experiment that do not have the same chance of occurrence are said to be not equally likely outcomes.
• All the outcomes of an experiment having an equal chance of occurrence are known as equally likely outcomes.
• The probability of a sure event is 1.
• The probability of an impossible event is 0.
• The probability of any event lies between 0 and 1.
• Probability of occurrence of an event + Probability of non-occurrence of an event = 1 .

Answer 2

Answer:

(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)

Thus, total number of outcomes of throwing two dice simultaneously = 36

Let the event of getting the sum of the numbers on the dice as 8 be E.

The outcomes where the sum of the numbers is 8 are: (6, 2) (5, 3), (4, 4) (4, 4), (3, 5) , (2, 6)

Therefore Number of favourable outcomes for occurrence of event E = 5

So, probability of getting the sum as 8.

Probability = 5/36.