Question

An unbiased die is thrown. What is probability of getting : (i) An even number (ii) An odd number (iii) A multiple of 3 (iv) a number 3 or 4 (v) an even number and multiple of 3 (vi) a number between 3 and 6 (vii) A number greater than 3 (viii) A number less than 4 Select the correct answer from above options

Answer 1

When a die is thrown, all possible outcomes are 1,2,3,4,5,6. Total number of possible outcomes = 6. (I) Let E1 be the event of getting a 3. Then, the number of favourable outcomes = 1. ∴ P(getting a 3) =P(E1)= 1 6 . (ii) Let E2 be the event of getting a 5. Then, the number of favourable outcomes = 1. ∴ P(getting a 5)P(E2)= 1 6 . (iii) Let E3) be the event of getting an odd number. Then, the favourable outcomes are 1, 3, 5. Number of favourable outcomes = 3. ∴ P(getting an old number ) =P(E3)= 3 6 = 1 2 . (iv) Let E4 be the event of getting a number greater than 4. Then, the favourable outcomes are 5, 6. Number of favourable outcomes = 2. ∴ P(getting a number greater than 4) P(E4)= 2 6 = 1 3 .