Practice AP Inter 1st Year Maths Study Material Chapter 14 Probability MCQ to identify your strengths and weak areas.
AP Inter 1st Year Maths Probability MCQ
Question 1.
Let A and B be two events such that P(A) = 0.8, P(B) = 0.7. Then P (A ∩ B).
1) ≤ 0.6
2) ≥ 0.5
3) ≥ 0.7
4) ≤ 0.4
Answer:
2) ≥ 0.5
Explanation:
Given : P(A) = 0.8, P(B) = 0.7
We know that P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
So, P(A ∩ B) = P(A) + P(B) – P(A ∪ B)
Maximum P(A ∪ B) = 1 ⇒ P(A ∩ B) = 0.8 + 0.7 – 1 = 0.5
Question 2.
The probability that a leap year selected at random will contain 53 Sundays is
(1) \(\frac{1}{7}\)
(2) \(\frac{2}{7}\)
(3) \(\frac{6}{7}\)
(4) \(\frac{5}{7}\)
Answer:
(2) \(\frac{2}{7}\)
Explanation:
Leap year has 366 days = 52 weeks + 2 days
So, it will have 53 Sundays if :
The two extra days are (Sunday and Monday) or (Saturday and Sunday) out of 7 possible day pairs; 2 pairs contain Sunday ⇒ Probability = \(\frac{2}{7}\).
Question 3.
If two dice are thrown, then the probability of getting the same number on both the faces is
(1) \(\frac{2}{6}\)
(2) \(\frac{3}{6}\)
(3) \(\frac{5}{6}\)
(4) \(\frac{1}{6}\)
Answer:
(4) \(\frac{1}{6}\)
Explanation:
Getting same number on both dice : (1, 1), (2, 2) ……….. (6, 6) outcomes.
Total outcomes = 36.
So, Probability = \(\frac{6}{36}=\frac{1}{6}\)
Question 4.
If two dice are thrown, then the probability of getting a total score of seven is
(1) \(\frac{1}{6}\)
(2) \(\frac{2}{6}\)
(3) \(\frac{3}{6}\)
(4) \(\frac{5}{6}\)
Answer:
(1) \(\frac{1}{6}\)
Explanation:
Total score of 7 means : (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) → 6 outcomes
Total outcomes = 36
So, Probability = \(\frac{6}{36}=\frac{1}{6}\)
Question 5.
If A and B are two events of a sample space with P(AuB) = P(A) + P(B), then they are
1) Mutually exclusive
2) Exhaustive
3) 1 and 2
4) None of these
Answer:
1) Mutually exclusive
Explanation:
P(A ∪ B) = P(A) + P(B) means P(A ∩ B) = 0 ⇒ A and B are mutually exclusive.
Question 6.
An integer is picked from 1 to 20 (both inclusive). Then the probability that it is a prime
(1) \(\frac{3}{20}\)
(2) \(\frac{3}{5}\)
(3) \(\frac{2}{5}\)
(4) \(\frac{1}{5}\)
Answer:
(3) \(\frac{2}{5}\)
Explanation:
Total numbers from 1 to 20 = 20.
Prime numbers ≤ 20 = 2, 3, 5, 7, 11, 13, 17, 19 → 8 primes
Probability = \(\frac{8}{20}=\frac{2}{5}\)
Question 7.
If P(A) = 0.5, P(B) = 0.3. (given that A and B are mutually exclusive) Then P(A’ ∩ B’) =
1) 0.6
2) 0.5
3) 0.7
4) 0.2
Answer:
4) 0.2
Explanation:
A and B are mutually exclusive ⇒ P(A ∩ B) = 0
P(A ∪ B) = P(A) + P(B) = 0.5 + 0.3 = 0.8
Then P(A’ ∩ B ) = 1 – P(A ∪ B) = 1 – 0.8 = 0.2
Question 8.
One card is drawn at random from a well shuffled deck of 52 cards. Then the probability that the card be not a red card.
(1) \(\frac{2}{5}\)
(2) \(\frac{1}{5}\)
(3) \(\frac{1}{2}\)
(4) \(\frac{1}{3}\)
Answer:
(3) \(\frac{1}{2}\)
Explanation:
In a deck of 52 cards, 26 are red (13 hearts + 13 diamonds). so, not red = 26
Probability = \(\frac{26}{52}=\frac{1}{2}\)
Question 9.
Which of the following is false ?
1) P(E) = 0 ⇔ E is an impossible event.
2) 0 ≤ P(E) < 1.
3) P(E) = 1 ⇔ E is a certain event.
4) P(E) + P(Ē) = 1.
Answer:
2) 0 ≤ P(E) < 1.
Explanation:
Option 2 is False, because a probability can be exactly 1; it’s not strictly less than one.
Question 10.
Which of the following statement is not correct ? P is a probability function of the sample space S.
1) P(E) > 0 ∀ E ∈ P(S).
2) P(S) = 1.
3) P(Φ) = 0.
4) P(E1 ∩ E2) = P(E1) + P(E2) where E1, E2 are mutually exclusive.
Answer:
4) P(E1 ∩ E2) = P(E1) + P(E2) where E1, E2 are mutually exclusive.
Explanation:
Option 4 is incorrect. In general, P(E1 ∩ E2) ≠ P(E1) + P(E2)
This equality is invalid unless both probabilities are 0 (which isn’t mentioned)
So, this is the false statement.