A die is thrown once. Find the probability of getting : (a) a prime number (b) (b) a number between 3 and 6 (c) a number greater than 4 (d) a number at most 4 (e) a factor of 6.

Explanation

(i) As a die is rolled once, therefore there are six possible outcomes, i.e., 1,2,3,4,5,6.
(a) Let A be an event ''getting a prime number''.
Favourable cases for a prime number are 2,3,5,
`"i.e., "n(A)=3`
`"Hence "P(A)=(n(A))/(n(S))=(3)/(6)=(1)/(2)`
(b) Let A be an event ''getting a number between 3 and 6''.
Favourable cases for events A are 4 or 5.
`i.e.," "n(A)=2`
`P(A)=(n(A))/(n(S))=(2)/(6)=(1)/(3)`
(c) Let A be an event ''a number greater than 4''.
Favourable cases of events A are 5, 6.
`i.e.," "n(A)=2`
`P(A)=(n(A))/(n(S))=(2)/(6)=(1)/(3)`
(d) Let A be the event of getting a number at most 4.
`therefore" "A= {1,2,3}" "rArr" "n(A)=4,n(S)=6`
`therefore" Required probability "=(n(A))/(n(S))=(4)/(2)=(2)/(3)`
(e) Let A be the event of getting a factor of 6.
`therefore" "A={1,2,36}" "rArr" "n(A)=4, n(A)=6`
`therefore" Required probability "=(4)/(6)=(2)/(3)`