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Example 9: A die is thrown only once. Find the probability of getting:

( a) a prime number (b) a multiple of 2 (c) a factor of number 6
Solution: When we roll a die once, possible outcomes, S = {1, 2, 3, 4, 5, 6}
\ Total outcomes, n(S) = 6

( a) Prime numbers = 2, 3, 5. Thus, n(E) = 3
E
n() 3 1
\ P(getting a prime number) = = =
n() 6 2
S
( b) Multiples of 2 = 2, 4, 6. Thus, n(E) = 3
E
n() 3 1
\ P(getting a multiple of 2) = = =
n() 6 2
S
( c) Factors of number 6 = 1, 2, 3, 6. Thus, n(E) = 4
n() 4 2
E
\ P(getting a factor of number 6) = = =
n() 6 3
S
Example 10: Numbers 1 to 10 are written on 10 separate slips (one number on one slip) kept in
a box and mixed up well. One slip is chosen from the box without looking into it. What is the
probability of
( a) getting a number 4? (b) getting a number greater than 5?

( c) getting a number less than 7? (d) getting 2-digit number?
Solution: Possible outcomes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1
( a) Probability of getting a number 4 =
10
( b) Numbers greater than 5 = 6, 7, 8, 9, 10

5 1
\ Probability of getting a number greater than 5 = =
10 2
( c) Numbers less than 7 = 1, 2, 3, 4, 5, 6
6 3
\ Probability of getting a number less than 7 = 10 = 5

( d) 2-digit number = 10
1
\ Probability of getting 2-digit number =
10
Example 11: Suppose you spin the wheel
( a) List the number of outcomes of getting a green sector and not
getting a green sector on this wheel.
( b) Find the probability of getting a green sector.

( c) Find the probability of not getting a green sector.
Solution: (a) Q 5 G’s are there on the wheel

\ Number of outcomes of getting a green sector = 5
Q 3 R’s are there which are not G’s

\ Number of outcomes of not getting green sector = 3

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