All questions
- For the following experiment write sample space 'S' and number of sample points n(S): Two digit numbers are formed using digits 2, 3 and 5 without repeating a digit. Answer: S = 23, 25, 32, 35, 52, 53, n(S) = 6 The tens digit can be any of 2, 3, 5 (3 ways); the units digit is one of the remaining two (2 w... 1
- The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop. (The disc has six coloured parts: Red, Orange, Yellow, Blue, Green, Purple.) Answer: S = {Red, Orange, Yellow, Blue, Green, Purple}, n(S) = 6 The arrow can stop on any one of the six coloured parts of the disc, so eac... 1
- In the month of March 2019, find the days on which the date is a multiple of 5. (see the given page of the calender; 1st March 2019 was a Friday) Answer: S = {Tuesday, Sunday, Friday, Wednesday, Monday, Saturday}, n(S) = 6 Dates that are multiples of 5: 5, 10, 15, 20, 25, 30. Since 1st... 1
- Form a 'Road safety commitee' of two, from 2 boys (B1, B2) and 2 girls (G1, G2). Complete the following activity to write the sample space. Answer: S = {B₁B₂, G₁G₂, B₁G₁, B₁G₂, B₂G₁, B₂G₂}, n(S) = 6 (a) Committee of 2 boys: B₁B₂ (b) Committee of 2 girls: G₁G₂ (c) One boy and one... 1
- Write S, n(S) and events A, B, C with n(A), n(B), n(C): One die is rolled. A: Even number on the upper face. B: Odd number on the upper face. C: Prime number on the upper face. Answer: S = {1, 2, 3, 4, 5, 6}, n(S) = 6; A = {2, 4, 6}, n(A) = 3; B = {1, 3, 5}, n(B) = 3; C = {2, 3, 5}, n(C) = 3 The prime numbers from 1... 1
- Write S, n(S) and events A, B, C with n(A), n(B), n(C): Two dice are rolled simultaneously. A: sum of digits on upper faces is a multiple of 6. B: sum is minimum 10. C: same digit on both upper faces. Answer: n(S) = 36; n(A) = 6; n(B) = 6; n(C) = 6 S = (1,1), (1,2), ..., (1,6), (2,1), ..., (2,6), ..., (6,1), ..., (6,6), i.e. all ordered pa... 1
- Write S, n(S) and events A, B, C with n(A), n(B), n(C): Three coins are tossed simultaneously. A: To get at least two heads. B: To get no head. C: To get head on the second coin. Answer: n(S) = 8; n(A) = 4; n(B) = 1; n(C) = 4 S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, n(S) = 8 A (two or three heads) = {HHH, HHT, HT... 1
- Write S, n(S) and events A, B, C: Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition. A: number is even. B: number is divisible by 3. C: number is greater than 50. Answer: n(S) = 25; n(A) = 13; n(B) = 9; n(C) = 4 The tens digit cannot be 0, so it is one of 1 to 5 (5 ways), and the units digit is any of... 1
- Write S, n(S) and events A, B, C: From three men and two women, environment committee of two persons is to be formed. A: at least one woman member. B: one man, one woman. C: no woman member. Answer: n(S) = 10; n(A) = 7; n(B) = 6; n(C) = 3 Let the men be M₁, M₂, M₃ and the women F₁, F₂. S = {M₁M₂, M₁M₃, M₂M₃, M₁F₁, M₁F₂, M₂F₁, M₂F... 1
- Write S, n(S) and events A, B, C: One coin and one die are thrown simultaneously. A: head and an odd number. B: a head or tail and an even number. C: number on upper face greater than 7 and tail on the coin. Answer: n(S) = 12; n(A) = 3; n(B) = 6; n(C) = 0 S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, n(S) = 12 A = {H1, H3, H5}, n(A) = 3 B... 1
- If two coins are tossed, find the probability of the following events. (1) Getting at least one head. (2) Getting no head. Answer: (1) 3/4 (2) 1/4 S = HH, HT, TH, TT, n(S) = 4 (1) A = HH, HT, TH, n(A) = 3, so P(A) = 3/4 . (2) B = TT, n(B) = 1, so P(B) = 1/4 . 1
- If two dice are rolled simultaneously, find the probability: (1) sum of the digits on the upper faces is at least 10 (2) the sum is 33 (3) the digit on the first die is greater than the digit on second die. Answer: (1) 1/6 (2) 0 (3) 5/12 n(S) = 36. (1) Sum at least 10: A = (4,6), (5,5), (6,4), (5,6), (6,5), (6,6), n(A) = 6. P(A) = 6/36 = 1/6 (2)... 1
- There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn - (1) shows an even number. (2) shows a number which is a multiple of 5. Answer: (1) 7/15 (2) 1/5 n(S) = 15 (1) A = 2, 4, 6, 8, 10, 12, 14, n(A) = 7, P(A) = 7/15 . (2) B = 5, 10, 15, n(B) = 3, P(B) = 3/15 = 1/5 . 1
- A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is (1) an odd number? (2) a multiple of 5? Answer: (1) 4/5 (2) 1/5 Tens digit: 5 choices, units digit: 4 remaining choices, so n(S) = 5 × 4 = 20 . S = 23, 25, 27, 29, 32, 35, 37, 39,... 1
- A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is - (1) an ace. (2) a spade. Answer: (1) 1/13 (2) 1/4 n(S) = 52 (1) There are 4 aces: P(A) = 4/52 = 1/13 . (2) There are 13 spades: P(B) = 13/52 = 1/4 . 1
- Choose the correct alternative answer: Which number cannot represent a probability? Answer: (B) 1.5 Probability always lies between 0 and 1 (0% to 100%). 1.5 is greater than 1, so it cannot be a probability; 2/3 , 15% and 0.... 1
- Choose the correct alternative answer: A die is rolled. What is the probability that the number appearing on upper face is less than 3? Answer: (B) 1/3 Favourable outcomes: 1, 2. P = 2/6 = 1/3 . 1
- Choose the correct alternative answer: What is the probability of the event that a number chosen from 1 to 100 is a prime number? Answer: (C) 1/4 There are 25 prime numbers from 1 to 100 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79... 1
- Choose the correct alternative answer: There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5? Answer: (A) 1/5 Multiples of 5 up to 40: 5, 10, 15, 20, 25, 30, 35, 40 (8 numbers). P = 8/40 = 1/5 . 1
- Choose the correct alternative answer: If n(A) = 2, P(A) = 1/5, then n(S) = ? Answer: (A) 10 P(A) = n(A)/n(S) ⇒ 1/5 = 2/n(S) ⇒ n(S) = 10 . 1
- Basketball players John, Vasim, Akash were practising the ball drop in the basket. The probabilities of success for John, Vasim and Akash are 4/5, 0.83 and 58% respectively. Who had the greatest probability of success? Answer: Vasim Write all probabilities as decimals: John: 4/5 = 0.80 Vasim: 0.83 Akash: 58% = 0.58 Since 0.83 > 0.80 > 0.58, Vasim had the gr... 1
- In a hockey team there are 6 defenders, 4 offenders and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that - (1) The goalee will be selected. (2) A defender will be selected. Answer: (1) 1/11 (2) 6/11 n(S) = 6 + 4 + 1 = 11 (1) P(goalee) = 1/11 (2) P(defender) = 6/11 1
- Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card? Answer: 5/26 n(S) = 26. Vowels are a, e, i, o, u, so n(A) = 5. P(A) = 5/26 1
- If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero. Answer: Proved, t_(m+n) = 0 m[a + (m - 1)d] = n[a + (n - 1)d] a(m - n) + d[(m² - n²) - (m - n)] = 0 (m - n)[a + (m + n - 1)d] = 0 For m ≠ n... 1