Question

Two dice are rolled find probability
Digits on upper face of first die is less than the digit on second die
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Answer 1

Step-by-step explanation:

Given:-

Two dice are rolled

To find:-

Find probability that the digits on the upper face of the first die is less than the digit on the second die?

Solution:-

We know that

Two dice are rolled simultaneously then

The total possible outcomes 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)

Number of total possible outcomes = 36

among all the favourable outcome of the digit on the upper face of the first die is less than the digit on the second die=

(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),

(3,6),(4,5),(4,6),(5,6)

Total number of favourable outcomes = 15

Probability of an event E = P(E)

Number of favourable outcomes / Total number of all possible outcomes

=>15/36

=>(3×5)/(3×12)

=>5/12

The probability = 5/12

Answer:-

The probability of getting that the digits on the upper face of the first die is less than the digit on the second die = 5/12

Used formulae:-

• If two dice rolled simultaneously or a die is rolled twice then the total possible outcomes are 36
• If 'n' dice rolled once then the total possible outcomes are 6^2
• Number of favourable outcomes / Total number of all possible outcomes

Answer 2

Answer:

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