Solved Questions of Probability
1. A bag contains 5 red balls and 7 blue balls. If one ball is randomly selected from the bag, what is the probability that it is red?
a) 5/12
b) 5/14
c) 6/12
d) 8/14
Answer: a) 5/12
Explanation: There are a total of 12 balls in the bag (5 red + 7 blue).
The probability of selecting a red ball is 5/12 or 0.417 (5 out of 12).
2. A coin is flipped 3 times. What is the probability of getting 2 heads and 1 tail?
a) 3/2
b) 4/4
c) 4/6
d) 3/8
Answer: d) 3/8
Explanation: There are a total of 23 = 8 possible outcomes when flipping a coin 3 times (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).
The probability of getting 2 heads and 1 tail is 3/8 or 0.375 (3 out of 8 possible outcomes of HHT, HTH, THH).
3. A deck of cards contains 4 aces and 52 cards total. If one card is drawn from the deck, what is the probability of it being an ace?
a) 1/12
b) 1/14
c) 2/13
d) 1/13
Answer: d) 1/13
Explanation: There are 4 aces out of 52 total cards, so the probability of drawing an ace is 4/52 = 1/13 or 0.0769.
4. A bag contains 3 red marbles, 4 blue marbles and 5 green marbles. What is the probability of drawing a blue marble?
a) 1/2
b) 1/4
c) 1/3
d) 1/8
Answer: c) 1/3
Explanation: The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles in the bag.
In this case, there are 4 blue marbles out of 12 total marbles, so the probability is 4/12 or 1/3.
5. A coin is flipped twice. What is the probability of getting heads twice?
a) 2/2
b) 1/4
c) 1/6
d) 2/8
Answer: b) 1/4
Explanation: The probability of getting heads on a single coin flip is 1/2. To find the probability of getting heads twice, we multiply the probabilities of each event.
So, the probability of getting heads twice is (1/2) x (1/2) = 1/4.
6. A deck of cards contains 52 cards, 26 of which are red and 26 of which are black. If a card is drawn at random, what is the probability that it is a red card?
a) 1/2
b) 4/2
c) 2/6
d) 2/8
Answer: a) 1/2
Explanation: The probability of drawing a red card is the number of red cards divided by the total number of cards in the deck.
In this case, there are 26 red cards out of 52 total cards, so the probability is 26/52 or 1/2.
7. A box contains 6 white balls and 4 black balls. If a ball is drawn at random, what is the probability that it is white?
a) 2/3
b) 3/4
c) 3/5
d) 2/8
Answer: c) 3/5
Explanation: The probability of drawing a white ball is the number of white balls divided by the total number of balls in the box.
In this case, there are 6 white balls out of 10 total balls, so the probability is 6/10 or 3/5.
8. A die is rolled. What is the probability of getting a number greater than 4?
a) 2/3
b) 1/4
c) 2/6
d) 1/3
Answer: d) 1/3
Explanation: There are 6 possible outcomes when rolling a die, and 2 of them (5, 6) are greater than 4.
So, the probability of getting a number greater than 4 is 2/6 or 1/3.
Practice Questions of Probability
1. A bag contains 7 red balls and 5 blue balls. If a ball is randomly selected from the bag, what is the probability of it being red?
a) 7/12
b) 4/12
c) 2/16
d) 4/18
Answer: a) 7/12
2. A coin is flipped 5 times. What is the probability of getting heads at least once?
a) 37/32
b) 24/12
c) 32/16
d) 31/32
Answer: d) 31/32
3. A deck of cards contains 52 cards, including 4 aces. If a card is randomly selected from the deck, what is the probability of not getting an ace?
a) 17/12
b) 24/12
c) 12/13
d) 14/18
Answer: c) 12/13
4. A die is rolled twice. What is the probability of getting a 6 on both rolls?
a) 3/12
b) 4/22
c) 1/36
d) 4/28
Answer: c) 1/36
5. A bag contains 5 white marbles and 7 black marbles. If two marbles are randomly selected without replacement, what is the probability of both being white?
a) 5/33
b) 4/22
c) 2/66
d) 4/88
Answer: a) 5/33
6. A game involves rolling a fair die and drawing a card from a standard deck of cards. What is the probability of rolling a 6 and drawing a diamond card?
a) 1/12
b) 6/22
c) 2/26
d) 1/24
Answer: d) 1/24
7. A Card is drawn from a set of playing cards. What is the probability that the card drawn is a diamond card?
a) 7/1
b) 1/4
c) 2/6
d) 4/8
Answer: b) 1/4
8. A coin is flipped 8 times. What is the probability of getting tails exactly 3 times?
a) 7/32
b) 4/22
c) 7/16
d) 4/28
Answer: a) 7/32
9. A bag contains 5 white marbles and 3 black marbles. If three marbles are randomly selected without replacement, what is the probability of getting at least one of the three marbles drawn to be black, if the first marble is red?
a) 27/10
b) 44/12
c) 25/36
d) 43/18
Answer: c) 25/36
10. What is the probability of drawing a card that is not an ace from a well-shuffled deck of 52 cards?
a) 12/13
b) 11/12
c) 12/15
d) 11/14
Answer: a) 12/13
