(a) Find the probability that a number selected at random from the numbers 30, 31, 32, 33, ....., 60 is (i) a prime number (ii) a multiple of 6.
OR
(b) Slips of letters of the word 'BACKGROUND' are put in a bowl and thoroughly mixed. One slip is picked up at random. Find the probability that picked up slip's letter is (i) a vowel (ii) present in the word 'BALL'.
✅ Answer & Solution
**(a)** Total numbers from 30 to 60 = 31.
(i) Primes: 31, 37, 41, 43, 47, 53, 59 → 7 numbers. $$P=\frac{7}{31}$$
(ii) Multiples of 6: 30, 36, 42, 48, 54, 60 → 6 numbers. $$P=\frac{6}{31}$$
**(b)** BACKGROUND has 10 distinct letters: B,A,C,K,G,R,O,U,N,D.
(i) Vowels: A, O, U → 3 letters. $$P=\frac{3}{10}$$
(ii) Letters of 'BALL' are B, A, L. Of these, only B and A occur in BACKGROUND (L does not) → 2 letters. $$P=\frac{2}{10}=\frac15$$
✅ Verified by Super Admin
