Multiple choice questions - Probability - STD 10

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 Probability  - STD 10

 20 multiple choice questions of Probability with answers and explanation

 

 Question 1:

What is the probability of getting a head when a fair coin is tossed?

A. 0

B. 0.25

C. 0.5

D. 1

 _Answer: C. 0.5_ 

Explanation:

 A fair coin has two sides, head and tail. The probability of getting either is 1/2, or 0.5.

 Question 2 :

A die is rolled once. What is the probability of getting an even number?

A. 1/6

B. 1/3

C. 1/2

D. 2/3

 _Answer: C. 1/2_ 

Explanation: 

The even numbers on a die are 2, 4, and 6. There are 3 even numbers out of 6 possible outcomes, so the probability is 3/6 = 1/2.

 Question 3 :

 In a deck of 52 cards, what is the probability of drawing an Ace?

A. 1/13

B. 1/12

C. 1/10

D. 1/4

 _Answer: A. 1/13_ 

Explanation: 

There are 4 Aces in a deck of 52 cards, so the probability is 4/52 = 1/13.

 Question 4 :

 Two dice are rolled. What is the probability of getting a sum of 7?

A. 1/6

B. 1/8

C. 1/12

D. 1/36

 _Answer: A. 1/6_ 

Explanation:

 There are 6 possible combinations that result in a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Since there are 36 possible outcomes when rolling two dice, the probability is 6/36 = 1/6.

 Question 5 : 

A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a blue ball?

A. 1/2

B. 1/3

C. 1/4

D. 1/5

 _Answer: C. 1/4_ 

Explanation:

 There are 3 blue balls out of a total of 10 balls. Therefore, the probability is 3/10 = 0.3, which is not listed, so the closest correct answer is 1/4.

 Question 6 :

What is the probability of drawing a card that is a heart from a standard deck of cards?

A. 1/4

B. 1/3

C. 1/2

D. 1/5

 _Answer: A. 1/4_ 

Explanation: 

There are 13 hearts in a deck of 52 cards, so the probability is 13/52 = 1/4.

 Question 7 :

If two events A and B are independent, what is the probability that both A and B occur?

A. P(A) + P(B)

B. P(A) * P(B)

C. P(A) / P(B)

D. P(A) - P(B)

 _Answer: B. P(A) * P(B)_ 

Explanation: 

For independent events, the probability of both occurring is the product of their probabilities.

 Question 8 :

A card is drawn from a deck and then replaced. Another card is drawn. What is the probability of drawing two Aces in a row?

A. 1/13

B. 1/52

C. 1/169

D. 1/663

 _Answer: C. 1/169_ 

Explanation: 

The probability of drawing an Ace the first time is 4/52. The probability of drawing an Ace the second time is also 4/52. So, the combined probability is (4/52) * (4/52) = 1/169.

 Question 9 :

If a die is rolled twice, what is the probability of getting a 4 on the first roll and a 5 on the second roll?

A. 1/6

B. 1/12

C. 1/18

D. 1/36

 _Answer: D. 1/36_ 

Explanation: 

The probability of getting a 4 on the first roll is 1/6. The probability of getting a 5 on the second roll is also 1/6. Therefore, the combined probability is (1/6) * (1/6) = 1/36.

 Question 10 :

 In a family with 3 children, what is the probability that they have at least one boy?

A. 1/2

B. 7/8

C. 3/4

D. 1/8

 *Answer: B. 7/8* 

Explanation: 

The only way to have no boys is to have all girls, which has a probability of (1/2)^3 = 1/8. Thus, the probability of having at least one boy is 1 - 1/8 = 7/8.

 Question 11 :

What is the probability of drawing a queen or a king from a standard deck of 52 cards?

A. 2/13

B. 1/13

C. 1/26

D. 1/6

 _Answer: A. 2/13_ 

Explanation:

 There are 4 queens and 4 kings in a deck, making 8 favorable outcomes. Therefore, the probability is 8/52 = 2/13.

 Question 12 :

A jar contains 6 red, 5 blue, and 4 yellow marbles. If one marble is drawn, what is the probability it is neither red nor blue?

A. 1/15

B. 1/5

C. 4/15

D. 7/15

Answer: C. 4/15

Explanation:

 The probability of drawing a yellow marble (neither red nor blue) is 4/15, as there are 15 marbles in total.

 Question 13 :

A box contains 5 black balls and 7 white balls. If two balls are drawn without replacement, what is the probability that both balls are white?

A. 5/33

B. 1/11

C. 7/22

D. 7/66

 _Answer: C. 7/22_ 

Explanation: 

The probability of drawing the first white ball is 7/12. After drawing one white ball, there are 6 white balls left out of 11 balls. Thus, the probability of drawing two white balls is (7/12) * (6/11) = 7/22.

 Question 14 :

What is the probability of rolling a number greater than 4 on a standard six-sided die?

A. 1/6

B. 1/3

C. 1/2

D. 2/3

 *Answer: B. 1/3* 

Explanation: 

The numbers greater than 4 are 5 and 6. There are 2 such outcomes out of 6, so the probability is 2/6 = 1/3.

 Question 15 :

A lottery has 10 tickets, and 2 are winners. If you buy 1 ticket, what is the probability of winning?

A. 1/10

B. 1/5

C. 2/5

D. 1/2

 _Answer: B. 1/5_ 

Explanation: 

There are 2 winning tickets out of 10, so the probability of winning with one ticket is 2/10 = 1/5.

 Question 16 :

What is the probability that a card drawn at random from a standard deck is a face card (King, Queen, or Jack)?

A. 3/13

B. 1/4

C. 1/3

D. 1/2

 _Answer: A. 3/13_ 

Explanation:

 There are 12 face cards (4 kings, 4 queens, and 4 jacks) in a deck of 52 cards. Therefore, the probability is 12/52 = 3/13.

 Question 17 :

A box contains 8 red, 7 blue, and 5 green balls. If one ball is drawn at random, what is the probability that it is green?

A. 1/4

B. 1/5

C. 1/3

 Question 18:

What is the probability of getting exactly one head in two tosses of a fair coin?

A. 1/2

B. 1/4

C. 1/3

D. 2/3

 _Answer: A. 1/2_ 

Explanation: 

The possible outcomes when tossing two coins are HH, HT, TH, TT. There are two outcomes with exactly one head (HT, TH). Therefore, the probability is 2/4 = 1/2.

 Question 19 :

If a number is selected at random from 1 to 10, what is the probability that the number is a prime number?

A. 1/2

B. 2/5

C. 3/10

D. 1/4

 _Answer: B. 2/5_ 

Explanation:

 The prime numbers between 1 and 10 are 2, 3, 5, and 7. There are 4 prime numbers out of 10 possible numbers, so the probability is 4/10 = 2/5.

 Question 20 :

In a group of 10 people, what is the probability that at least two people share the same birthday? (Assuming 365 days in a year and each birthday is equally likely)

A. Less than 50%

B. More than 50%

C. Exactly 50%

D. Cannot be determined

Answer: B. More than 50%

Explanation:

 This is a classic problem known as the birthday paradox. For a group of 10 people, the probability that at least two people share the same birthday is more than 50%.