Vardaan Learning Institute
Master Notes: Probability
SECTION A: OBJECTIVE TYPE QUESTIONS
1. Probability of impossible event is:
Ans: (b) 0
2. P(not E) when P(E)=0.05:
Ans: (b) 0.95
$1 - 0.05 = 0.95$.
3. Probability of face card:
Ans: (b) 3/13
12 face cards in 52. $12/52 = 3/13$.
4. Which cannot be probability?:
Ans: (b) -1.5
Probability cannot be negative.
5. Probability of prime number on die:
Ans: (a) 1/2
Primes: 2, 3, 5. (3 numbers). $3/6 = 1/2$.
6. At most one head (Two coins):
Ans: (c) 3/4
Outcomes: {HT, TH, TT}. 3 outcomes. $3/4$.
7. Probability of event that cannot occur:
Ans: (d) 0
8. Number of rotten apples if P=0.18, Total=900:
Ans: (c) 162
$No = 0.18 \times 900 = 162$.
9. Bad eggs P=0.035, Total=400:
Ans: (b) 14
$No = 0.035 \times 400 = 14$.
10. 53 Sundays in non-leap year:
Ans: (a) 1/7
365 days = 52 weeks + 1 day. 1 day can be any of 7 days. P(Sunday) = 1/7.
SECTION B: SHORT ANSWER TYPE QUESTIONS
11. Bag with 3 Red, 5 Black.
Ans: (i) 3/8 (ii) 5/8
(i) Red: 3/8. (ii) Not Red: 1 - 3/8 = 5/8.
12. Die thrown once.
Ans: (i) 1/2 (ii) 1/2
(i) Between 2 and 6 (3,4,5): 3/6 = 1/2.
(ii) Odd (1,3,5): 3/6 = 1/2.
13. Cards: Red King, Spade.
Ans: (i) 1/26 (ii) 1/4
(i) Red Kings (2): 2/52 = 1/26.
(ii) Spades (13): 13/52 = 1/4.
14. Vowel from ASSASSINATION.
Ans: 6/13
Total 13. Vowels (A,A,A,I,A,I,O) = 6.
SECTION C: SHORT ANSWER TYPE II QUESTIONS
15. Discs 1-90.
Ans: (i) 9/10 (ii) 1/10 (iii) 1/5
(i) 2-digit (10-90): 81 numbers. 81/90 = 9/10.
(ii) Perfect square (1,4,9..81): 9 numbers. 9/90 = 1/10.
(iii) Div by 5 (5..90): 18 numbers. 18/90 = 1/5.
16. Piggy Bank Coins.
Ans: (i) 5/9 (ii) 17/18
Total 180 coins.
(i) 50p (100): 100/180 = 5/9.
(ii) Not 5Rs (170): 170/180 = 17/18.
17. Two dice sum.
Ans: (i) 5/36 (ii) 0 (iii) 1
(i) Sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) -> 5 outcomes.
(ii) Sum 13: Impossible.
(iii) Sum <= 12: Sure event.
18. 5 Diamond Cards.
Ans: (i) 1/5 (ii)(a) 1/4 (ii)(b) 0
(i) One Queen in 5 cards: 1/5.
(ii) Queen removed, 4 cards left (10,J,K,A).
(a) Ace: 1/4.
(b) Queen: 0/4 = 0.
19. Marbles: 3 Blue, 2 White, 4 Red.
Ans: (i) 2/9 (ii) 1/3 (iii) 4/9
Total = 9.
(i) White: 2/9.
(ii) Blue: 3/9 = 1/3.
(iii) Red: 4/9.
20. 144 Pens (20 def, 124 good).
Ans: (i) 31/36 (ii) 5/36
(i) Buy (Good): 124/144 = 31/36.
(ii) Not Buy (Defective): 20/144 = 5/36.
SECTION D: LONG ANSWER TYPE QUESTIONS
21. Jar with 24 marbles. P(Green) = 2/3.
Blue = 8, P(Blue new) = 2/7
Number of Green marbles = $\frac{2}{3} \times 24 = 16$.
Number of Blue marbles = $24 - 16 = 8$.
If 4 more Green added: Total = $24 + 4 = 28$.
Green = $16 + 4 = 20$. Blue = 8 (unchanged).
P(Blue) = $8/28 = 2/7$.
22. Deck with J, Q, K removed.
Ans: (i) 1/10 (ii) 3/10 (iii) 3/5 (iv) 2/5 (v) 0
Removed 12 face cards. Total remaining = $52 - 12 = 40$.
Remaining cards (per suit): A, 2, 3, 4, 5, 6, 7, 8, 9, 10.
(i) Value 7: 4 cards. $4/40 = 1/10$.
(ii) Value > 7 (8, 9, 10): $3 \times 4 = 12$ cards. $12/40 = 3/10$.
(iii) Value < 7 (A, 2, 3, 4, 5, 6): $6 \times 4=24$ cards. $24/40=3/5$.
(iv) Prime (2, 3, 5, 7): $4 \times 4 = 16$ cards. $16/40 = 2/5$.
(v) Face card: 0 cards. $0/40 = 0$.
SECTION E: CASE STUDY ANSWERS
23. Case Study: Spinner Game
(i) Sample Space (12): {1R, 1B, 1G, 1Y, 2R, 2B, 2G, 2Y, 3R, 3B, 3G, 3Y}.
(ii) Even(2) & Red: {2R} -> 1/12.
(iii) Num < 3 (1,2) & Not Yellow (R,B,G): {1R,1B,1G,2R,2B,2G} -> 6/12 = 1/2.
(iv) Odd (1,3) & Primary (R,B,Y): {1R,1B,1Y, 3R,3B,3Y} -> 6/12 = 1/2.
Ans: (i) Set (ii) 1/12 (iii) 1/2 (iv) 1/2