QQuestion
The letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter:
(a) of the word MONDAY?
(b) which does not appear in MONDAY?
(c) which appears both in SUNDAY and MONDAY?
✓Answer
The cards contain {A, D, M, N, O, S, U, Y}.
Total number of cards = 8.
(a) The letters of MONDAY present on the cards are {M, O, N, D, A, Y}.
Number of favourable cards = 6.
Required probability = \frac{6}{8}
⇒ Required probability = \frac{3}{4}
(b) The cards whose letters do not appear in MONDAY are {S, U}.
Number of favourable cards = 2.
Required probability = \frac{2}{8}
⇒ Required probability = \frac{1}{4}
(c) The letters that appear in both SUNDAY and MONDAY are {N, D, A, Y}.
Number of favourable cards = 4.
Required probability = \frac{4}{8}
⇒ Required probability = \frac{1}{2}
Related Questions
More ICSE Moderate level questions
Assertion (A): A die is thrown once and the probability of getting an even number is 2/3. Reason (R): The sample space for even numbers on a die is {2, 4, 6}. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true. (d) Both A and R are false.
A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.
A letter is chosen at random from all the letters of the English alphabet. The probability that the letter chosen is a vowel is: (a) (b) (c) (d)
Which of the following cannot be the probability of an event? (a) (b) 0.25 (c) (d) 67%
Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 − n). Find: (a) its first term and common difference. (b) the sum of its first 25 terms.
The following table gives the duration of movies in minutes: Duration (minutes) Number of movies 100–110 5 110–120 10 120–130 17 130–140 8 140–150 6 150–160 4 Using the step-deviation method, find the mean duration of the movies.
(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k. (b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).
The polynomial 3x³ + 8x² − 15x + k has (x − 1) as a factor. Find the value of k. Hence, factorize the resulting polynomial completely.
Suresh has a recurring deposit account in a bank. He deposits ₹2000 per month and the bank pays interest at the rate of 8% per annum. If he gets ₹1040 as interest at the time of maturity, find in years the total time for which the account was held.
Factorize: sin³ θ + cos³ θ. Hence, prove the identity:
Rohan bought the following eatables for his friends: S. No. Item Price Quantity Rate of GST 1 Laddu ₹500 per kg 2 kg 5% 2 Pastries ₹100 per piece 12 pieces 18% Calculate: (a) the total GST paid. (b) the total bill amount including GST.