## Chapter 14 Probability Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.

If P(E) = 0.82 then p(\(\overline{\mathbf{E}}\)) = …………. .

A) 0.18

B) 0.28

C) 0.38

D) P(E) = P(\(\overline{\mathbf{E}}\))

Answer:

A) 0.18

Question 2.

When an unbiased die is rolled once, what is the probability of getting a prime number out of all possible out- comes ?

A) 1

B) \(\frac{1}{2}\)

C) \(\frac{1}{3}\)

D) \(\frac{1}{6}\)

Answer:

B) \(\frac{1}{2}\)

Question 3.

Let E, E be the complimentary events, in a random experiment, then which of the following is true ?

A) P(E) + P(\(\overline{\mathbf{E}}\)) = 2

B) P(E) + P(\(\overline{\mathbf{E}}\)) = 3

C) P(\(\overline{\mathbf{E}}\)) + P(E) = 1

D) P(E) + P(\(\overline{\mathbf{E}}\)) – 4

Answer:

C) P(\(\overline{\mathbf{E}}\)) + P(E) = 1

Question 4.

Which one of the following cannot be the probability of an event ?

A) \(\frac{2}{3}\)

B) \(\frac{4}{5}\)

C) 0.7

D) \(\frac{5}{4}\)

Answer:

D) \(\frac{5}{4}\)

Question 5.

On random selection, the probability of getting a composite number among the numbers from 51 to 100.

A) \(\frac{4}{5}\)

B) \(\frac{1}{5}\)

C) \(\frac{3}{5}\)

D) \(\frac{2}{5}\)

Answer:

A) \(\frac{4}{5}\)

Question 6.

Let E and \(\overline{\mathbf{E}}\) be the complementary events. If P (E) = 0.65, then P (E) = ………………. .

A) 0.40

B) 0.45

C) 0.35

D) 0.30

Answer:

C) 0.35

Question 7.

At what value of ‘x’, \(\frac{5}{\mathbf{x}}\) may possible probability of an event ?

A) 2

B) 1

C) 4

D) 6

Answer:

D) 6

Question 8.

If P(E) is the probability of an event E, then ……………. .

A) 0 < P(E) < 1

B) 0 ≤ P(E) < 1

C) 0 ≤ P(E) ≤ 1

D) 0 < P(E) ≤ 1

Answer:

C) 0 ≤ P(E) ≤ 1

Question 9.

The probability of an event P(E) is always ……………… .

A) 0 ≤ P(E) ≤ 1

B) P(E) < 1

C) P(E) ≥ 1

D) P(E) ≤ 0

Answer:

A) 0 ≤ P(E) ≤ 1

Question 10.

The probability of getting right answer to a question is 0.68, the probability of getting a wrong answer is ……………… .

A) 0.32

B) 32%

C) 32

D) A and B

Answer:

D) A and B

Question 11.

A letter is choosen from the word “BAHUBALI”, the probability that it was not a vowel is

A) \(\frac{1}{2}\)

B) \(\frac{3}{2}\)

C) \(\frac{4}{3}\)

D) \(\frac{3}{4}\)

Answer:

A) \(\frac{1}{2}\)

Question 12.

The probability of sure event is

A) 0

B) 1/2

C) 1

D) Undefined

Answer:

C) 1

Question 13.

A dice is thrown once. The probability of getting a prime number is

A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{2}{3}\)

D) \(\frac{1}{6}\)

Answer:

B) \(\frac{1}{2}\)

Question 14.

From a set of single digit natural numbers, if a number chosen at random, then the probability that the number chosen is a multiple of 2, is

A) \(\frac{4}{9}\)

B) \(\frac{1}{3}\)

C) \(\frac{9}{4}\)

D) \(\frac{2}{5}\)

Answer:

A) \(\frac{4}{9}\)

Question 15.

If P(E) the probability of an event, then

A) P(E) ≥ 1

B) P(E) ≤ 0

C) 0 ≤ P(E) ≤ 1

D) P(E) ≤ 1

Answer:

C) 0 ≤ P(E) ≤ 1

Question 16.

If E and \(\overline{\mathbf{E}}\) are complementary events in a random experiment and P(E) = 0.3, the value of P(E) is …………….. .

A) 0.3

B) 0.7

C) 1

D) 0

Answer:

B) 0.7

Question 17.

If one letter is selected randomly from the letters of the word “COVID”, then the probability of getting a vowel is ……………….. .

A) \(\frac{4}{5}\)

B) \(\frac{3}{5}\)

C) \(\frac{2}{5}\)

D) \(\frac{1}{5}\)

Answer:

C) \(\frac{2}{5}\)

Question 18.

A fish tank has 5 male fish and 8 female fish. If a fish is randomly taken out of it, then the probability of getting a male fish is ……………… .

A) \(\frac{5}{8}\)

B) \(\frac{5}{13}\)

C) \(\frac{8}{5}\)

D) \(\frac{13}{5}\)

Answer:

B) \(\frac{5}{13}\)

Question 19.

In a random experiment E and \(\overline{\mathbf{E}}\) are complementary events. If P(E) = 0.43, then P(\(\overline{\mathbf{E}}\)) is ……………… .

A) 0.57

B) 0.43

C) 0.17

D) 1

Answer:

A) 0.57

Question 20.

Which of the following cannot be probability of an event ?

A) 0.35

B) 40%

C) 1 \(\frac{1}{2}\)

D) \(\frac{2}{3}\)

Answer:

C) 1 \(\frac{1}{2}\)

Question 21.

When a dice is thrown once, the probability of getting an even number less than 4 is

A) 1/4

B) 0

C) 1/2

D) 1/6

Answer:

D) 1/6

Question 22.

Two dice are rolled together. What is the probability of getting a sum greater than 10?

A) \(\frac{1}{9}\)

B) \(\frac{1}{6}\)

C) \(\frac{1}{12}\)

D) \(\frac{5}{18}\)

Answer:

C) \(\frac{1}{12}\)

Question 23.

Which of the following numbers cannot be the probability of happening of an even?

A) 0

B) \(\frac{7}{0.01}\)

C) 0.07

D) \(\frac{0.07}{3}\)

Answer:

B) \(\frac{7}{0.01}\)

Question 24.

A bag contains 5 red balls and n green balls. If the probability of drawing a green ball is three times that of a red ball, then the value of n is :

A) 18

B) 15

C) 10

D) 20

Answer:

B) 15

Question 25.

Assertion (A) : The probability that a leap year has 53 Sundays is \(\frac{2}{7}\) .

Reason (R) : The probability that a nonleap year has 53 Sundays is \(\frac{5}{7}\) .

A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

C) Assertion (A) is true, but Reason (R) is false.

D) Assertion (A) is false, but Reason (R) is true.

Answer:

B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Question 26.

One card is drawn at random from a well shuffled deck of 52 playing cards. What is the probability of getting 4 of hearts’?

A) \(\frac{1}{52}\)

B) \(\frac{1}{13}\)

C) \(\frac{1}{26}\)

D) \(\frac{1}{6}\)

Answer:

D) \(\frac{1}{6}\)

Question 27.

Assertion (A) : When two coins are tossed together, the probability of getting no tail is \(\frac{1}{4}\).

Reason (R) : The probability P(E) of an event E satisfies 0 ≤ P(E) ≤ 1.

A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

C) Assertion (A) is true, but Reason (R) is false.

D) Assertion (A) is false, but Reason (R) is true.

Answer:

B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Question 28.

For an event E, P(E) + P(\(\overline{\mathbf{E}}\) ) = x, then the value of x^{2} – 3 is

A) -2

B) 2

C) 1

D) -1

Answer:

A) -2

Question 29.

The probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is

A) \(\frac{9}{13}\)

B) \(\frac{35}{52}\)

C) \(\frac{10}{13}\)

D) \(\frac{19}{26}\)

Answer:

A) \(\frac{9}{13}\)

Question 30.

The probability of getting an even number, when a die is thrown once is

A) \(\frac{1}{2}\)

B) \(\frac{1}{3}\)

C) \(\frac{1}{6}\)

D) \(\frac{5}{6}\)

Answer:

A) \(\frac{1}{2}\)

Question 31.

Let E be an event such that P(not E) = \(\frac{1}{5}\), then P(E) is equal to :

A) \(\frac{1}{5}\)

B) \(\frac{2}{5}\)

C) 0

D) \(\frac{4}{5}\)

Answer:

A) \(\frac{1}{5}\)

Question 32.

From a well-shuffled deck of 52 cards, a card is drawn at random. What is the probability of getting king of hearts?

A) \(\frac{1}{52}\)

B) \(\frac{1}{26}\)

C) \(\frac{1}{13}\)

D) \(\frac{12}{13}\)

Answer:

B) \(\frac{1}{26}\)

Question 33.

The probability of an impossible event is

A) 1

B) \(\frac{1}{2}\)

C) not defined

D) 0

Answer:

D) 0

Question 34.

A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball?

A) \(\frac{1}{4}\)

B) \(\frac{2}{5}\)

C) \(\frac{7}{20}\)

D) \(\frac{13}{20}\)

Answer:

C) \(\frac{7}{20}\)

Question 35.

A card is drawn at random horn a well shuffled deck of 52 playing cards. The probability of getting a face card is

A) \(\frac{1}{2}\)

B) \(\frac{3}{13}\)

C) \(\frac{4}{13}\)

D) \(\frac{1}{13}\)

Answer:

B) \(\frac{3}{13}\)

Question 36.

A card is selected at random from a well shuffled deck of 52 cards. The probability of its being a red face card is

A) \(\frac{3}{26}\)

B) \(\frac{3}{13}\)

C) \(\frac{2}{13}\)

D) \(\frac{1}{2}\)

Answer:

A) \(\frac{3}{26}\)

Question 37.

One card is drawn at random from a well-shuffled deck of 52 playing cards. What is the probability of getting a black king?

A) \(\frac{1}{26}\)

B) \(\frac{1}{13}\)

C) \(\frac{1}{52}\)

D) \(\frac{1}{2}\)

Answer:

C) \(\frac{1}{52}\)