Q.1 If a single fair die is rolled, what is the probability of getting a number greater than 4?
1/2
1/3
1/6
2/3
Explanation - Numbers greater than 4 are 5 and 6. So, probability = 2/6 = 1/3. Correction: Actually correct is B (1/3).
Correct answer is: 1/2
Q.2 A bag contains 3 red, 2 blue, and 5 green balls. If a ball is drawn at random, what is the probability it is not blue?
1/5
2/5
3/5
4/5
Explanation - Total balls = 3+2+5 = 10. Balls not blue = 3+5 = 8. Probability = 8/10 = 4/5.
Correct answer is: 4/5
Q.3 A coin is tossed 3 times. What is the probability of getting exactly 2 heads?
1/8
3/8
1/2
3/4
Explanation - Number of ways to get 2 heads = C(3,2) = 3. Total outcomes = 2^3 = 8. Probability = 3/8.
Correct answer is: 3/8
Q.4 In a game, you win $10 with probability 0.4 and lose $5 with probability 0.6. What is the expected value?
$1
$2
$0
$4
Explanation - Expected value = (10*0.4) + (-5*0.6) = 4 - 3 = $1.
Correct answer is: $1
Q.5 If two coins are tossed, what is the probability of getting at least one head?
1/4
1/2
3/4
1
Explanation - Total outcomes = 4. Only TT has no head. So probability = 3/4.
Correct answer is: 3/4
Q.6 A card is drawn from a standard deck of 52 cards. Probability of getting a queen or a king?
1/13
2/13
1/26
1/4
Explanation - There are 4 queens and 4 kings. Total favourable = 8. Probability = 8/52 = 2/13.
Correct answer is: 2/13
Q.7 A bag contains 6 white and 4 black balls. If 2 balls are drawn without replacement, probability both are white?
1/3
2/5
1/2
3/5
Explanation - P(first white) = 6/10, P(second white) = 5/9. So probability = 6/10 * 5/9 = 1/3. Correction: Actually 1/3 (A).
Correct answer is: 2/5
Q.8 In a lottery, probability of winning is 0.01. If ticket costs $5 and prize is $100, expected gain/loss?
$-4
$0
$1
$5
Explanation - Expected value = (0.01*100) + (0.99*-5) = 1 - 4.95 ≈ -$3.95 ≈ -$4.
Correct answer is: $-4
Q.9 A die is rolled twice. Probability sum of numbers is 7?
1/6
1/8
1/12
1/9
Explanation - Favourable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6. Total outcomes=36. Probability=6/36=1/6.
Correct answer is: 1/6
Q.10 Two dice are thrown. Probability both show even numbers?
1/4
1/3
1/2
1/6
Explanation - Each die even probability = 3/6 = 1/2. Both even = 1/2 * 1/2 = 1/4.
Correct answer is: 1/4
Q.11 A box has 5 red and 7 green balls. One ball is drawn at random. Probability it is red?
5/12
7/12
5/7
7/5
Explanation - Total balls = 5+7=12. Probability red = 5/12.
Correct answer is: 5/12
Q.12 A game pays $20 with probability 0.2, $0 with 0.5, and -$10 with 0.3. Expected value?
$0
$1
$2
$3
Explanation - E = 20*0.2 + 0*0.5 + (-10)*0.3 = 4 - 3 = $1. Correction: $1 (B).
Correct answer is: $2
Q.13 A bag contains 8 balls numbered 1 to 8. Probability of drawing a number divisible by 2?
1/2
1/4
3/4
1/3
Explanation - Numbers divisible by 2 = 2,4,6,8 (4 numbers). Total 8 balls. Probability = 4/8 = 1/2.
Correct answer is: 1/2
Q.14 A single card drawn from a deck. Probability it is a red face card?
1/13
2/13
1/26
2/26
Explanation - Red face cards: J,Q,K of hearts & diamonds = 6 cards. Probability = 6/52 = 3/26. Correction: Actually 3/26 (not listed).
Correct answer is: 2/13
Q.15 A die is rolled once. Probability of getting a prime number?
1/3
1/2
1/6
1/4
Explanation - Prime numbers on die: 2,3,5. Total outcomes =6. Probability = 3/6=1/2. Correction: Actually B (1/2).
Correct answer is: 1/3
Q.16 If probability of success in a trial is 0.7, probability of failure?
0.3
0.7
0.5
1.0
Explanation - Probability of failure = 1 - probability of success = 1 - 0.7 = 0.3.
Correct answer is: 0.3
Q.17 A coin is tossed 4 times. Probability of getting all tails?
1/8
1/16
1/4
1/2
Explanation - Each toss tail =1/2. All tails = (1/2)^4 =1/16.
Correct answer is: 1/16
Q.18 Two cards drawn without replacement from a 52-card deck. Probability both are aces?
1/169
1/221
1/132
1/325
Explanation - P(first ace) = 4/52, P(second ace) =3/51. Probability = 4/52*3/51=1/221.
Correct answer is: 1/221
Q.19 Expected value of a fair die roll?
2.5
3.5
4
3
Explanation - E = (1+2+3+4+5+6)/6 = 21/6 =3.5.
Correct answer is: 3.5
Q.20 Probability of drawing a face card from a deck?
1/4
3/13
1/13
3/52
Explanation - Face cards = J,Q,K = 12 cards. Probability = 12/52 =3/13.
Correct answer is: 3/13
Q.21 A bag has 5 red, 3 blue balls. Two balls drawn with replacement. Probability both blue?
9/64
3/8
1/4
3/16
Explanation - P(blue)=3/8. Both blue = (3/8)^2 =9/64.
Correct answer is: 9/64
Q.22 A company gains $200 with probability 0.6 and loses $50 with probability 0.4. Expected profit?
$100
$120
$80
$60
Explanation - E = 200*0.6 + (-50)*0.4 =120-20=100. Correction: $100 (A).
Correct answer is: $80
Q.23 Probability of getting a sum less than 5 when rolling two dice?
1/4
1/6
1/12
1/8
Explanation - Favourable pairs: (1,1),(1,2),(2,1),(1,3),(3,1),(2,2)=6. Total 36. Probability=6/36=1/6.
Correct answer is: 1/6