A die has 6 faces marked by the given numbers as shown below: The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than – 3.
(iii) the smallest integer ?

Solution:

When a die is thrown, the possible outcomes are {1,2,3,-1,-2,-3}

Number of possible outcomes = 6

(i) Let E be the event of getting a positive integer.

Outcomes favourable to E are {1,2,3}

Number of favourable outcomes = 3

P(E) = 3/6 = 1/2

Hence the probability of getting a positive integer is ½.

(ii) Let E be the event of getting an integer greater than -3.

Outcomes favourable to E are { -2,-1,1,2,3}

Number of favourable outcomes = 5

P(E) = 5/6

Hence the probability of getting an integer greater than -3 is 5/6.

(iii) Let E be the event of getting the smallest integer.

Outcomes favourable to E is -3.

Number of favourable outcomes = 1

P(E) = 1/6

Hence the probability of getting the smallest integer is 1/6.