Probability MCQ Quiz - Objective Question with Answer for Probability - Download Free PDF

Given:

Blue balls = 3

Black balls = 4

Total balls = 3 + 4 = 7

Formula used:

Probability = Favourable outcomes ÷ Total outcomes

nCr = n! / [r!(n−r)!]

Calculations:

Ways to choose 2 blue balls = 3C2 = 3

Ways to choose any 2 balls from 7 = 7C2 = 21

⇒ P(2 blue) = 3 ÷ 21 = 1/7

Ways to choose 3 black balls = 4C3 = 4

Ways to choose any 3 balls from 7 = 7C3 = 35

⇒ P(3 black) = 4 ÷ 35

Difference = 1/7 - 4/35 = (5 - 4)/35 = 1/35

∴ The difference in probabilities is 1/35.

Calculation:

Word: FRACTION

Total letters = 8 (All are unique)

Identify vowels and consonants

Vowels = A, I, O ⇒ 3 vowels

Consonants = F, R, C, T, N ⇒ 5 consonants

Total number of arrangements without any restriction = 8! = 40320

All consonants must come together

Group all 5 consonants as 1 unit ⇒ Treat it as a single block

Now total = 1 consonant block + 3 vowels = 4 units

These 4 units can be arranged in 4! ways

Within the consonant block, the 5 consonants can be arranged among themselves in 5! ways

Total favorable arrangements = 4! × 5! = 24 × 120 = 2880

Required probability = Favorable outcomes ÷ Total outcomes

⇒ Probability = 2880 ÷ 40320 = 1 ÷ 14

Thus, the correct answer is 1/14.

Given:

A die has 6 faces with numbers 1, 2, 3, 4, 5, and 6.

We need to find the probability of getting a number greater than 3 when rolling a die once.

Formula Used:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Calculation:

Total number of outcomes = 6 (Numbers on the die: 1, 2, 3, 4, 5, 6)

Favorable outcomes (numbers greater than 3) = {4, 5, 6}

Number of favorable outcomes = 3

Probability = Number of favorable outcomes / Total number of outcomes

⇒ Probability = 3 / 6

⇒ Probability = 1 / 2

The probability of getting a number greater than 3 is 1/2.

Given:

P(A ∪ B') = 0.8

P(A) = 0.3

Formula used:

P(A ∪ B') = P(A) + P(B') - P(A ∩ B')

P(B') = 1 - P(B)

Calculations:

P(A ∪ B') = P(A) + (1 - P(B)) - P(A ∩ B')

Since A and B are independent, P(A ∩ B') = P(A) × P(B')

⇒ 0.8 = P(A) + 1 - P(B) - P(A) × P(B')

⇒ 0.8 = P(A) + 1 - P(B) - P(A) × (1 - P(B))

⇒ 0.8 = 0.3 + 1 - P(B) - 0.3 × (1 - P(B))

⇒ 0.8 = 0.3 + 1 - P(B) - 0.3 + 0.3P(B)

⇒ 0.8 - 1 = -P(B) + 0.3 × P(B)

⇒ -0.2 = -P(B)(1 - 0.3)

⇒ -0.2 = -P(B) × 0.7

⇒ P(B) = 0.2 ÷ 0.7

⇒ P(B) = 2/7

∴ P(B) = 2/7

Given:

Number of coins tossed = 4

Number of heads required = 2

Each coin has two outcomes: Head (H) or Tail (T).

Formula Used:

Probability of an event = (Number of favorable outcomes) / (Total number of outcomes)

Total outcomes for tossing n coins = 2ⁿ

Number of ways to get r heads in n tosses = nCr = n! / [r!(n - r)!]

Calculation:

Total number of outcomes = 2⁴ = 16

Number of ways to get exactly 2 heads = 4C2 = 4! / [2!(4 - 2)!]

⇒ 4C2 = (4 × 3) / (2 × 1)

⇒ 4C2 = 6

Probability of getting exactly 2 heads = (Number of favorable outcomes) / (Total number of outcomes)

⇒ Probability = 6 / 16

⇒ Probability = 3 / 8

The probability of getting exactly 2 heads is 3/8.

Probability of 3 students,

P(A) = 1/2, P(A̅) = 1/2

P(B) = 1/3, P(B̅) = 2/3

P(C) = 1/4, P(C̅) = 3/4

So, Probability of no one solve the question is =  = 1/4

⇒ P(None) = 1/4

Then, The probability to solve the question is = 1 - 1/4 = 3/4

Hence, the correct answer is "3/4".

Concept used:

Total number of spade cards = 13

Total number of diamond cards = 13

Formula used:

P = Favorable outcomes/Total outcomes 

Calculation:

Total outcomes = ⁵²C₂ =  =  = 1326

Favourable outcomes = ¹³C₁ × 13C1

= 13 × 13 = 169

∴ The Required Probability = 169/1326 = 13/102

Given:

Favorable outcomes are a multiple of 2 on one dice and a multiple of 3 on the other dice.

Concept used:

When two dice are thrown total outcome = 6 × 6 = 36

Probability = favourable outcomes/total outcomes

Explanation:

Favourable outcomes = (2,3), (4,3), (6,3), (2,6), (4,6), (6,6),

(3,2), (3,4), (3,6), (6,2), (6,4) = 11

Total outcomes = 6 × 6 = 36

∴ Probability = 11/36

Number of coins tossed = 4

∴ Sample space of four coins tossed = 2⁴ = 16

GIVEN:

One dice shows a multiple of 3.

Other dice shows even number.

CONCEPT:

Total number of outcomes in two dice is 36.

FORMULA USED:

P = Favorable outcomes/Total outcomes 

CALCULATION:
There are only 6 such cases as required,

(3,2), (3,4) (3,6) (6,2) (6,4) (6,6)

∴ Required probability = 6/36 = 1/6

∴ The probability is 1/6.

Given

Probability of passing the test by Sita = 60% = 60/100

Probability of passing the test by Gita = 40% = 40/100

Probability of passing the test by Mita = 20% = 20/100

Formula

Probability of not happening even A = 1 - Probability of  happening even A

Probability of happening A and B = Probability of happening A × Probability of happening B

Calculation

Probability of not passing the test by Mita = 1 - Probability of passing the test by Mita

= 1 - (20/100)

= 80/100

Now,

Probability that at Sita and Gita will pass the test and Mita will not = Probability of passing the test by Sita × Probability of passing the test by Gita × Probability of not passing the test by Mita

= (60/100) × (40/100) × (80/100)

= 192/1000

= (192/10)%

= 19.2%

Given

Number of black balls = 5

Number of white balls = 6

Formula

Probability = Favorable events/Total possible events

Calculation

Favorable event = ⁶C₂

Total possible events = ¹¹C₂

∴ Probability = ⁶C₂/¹¹C₂ = (6 × 5)/(11 × 10) = 3/11

Given:

Three coins are tossed simultaneously.

Formula:

Probability = Number of favorable outcomes/ Total number of outcomes.

Calculation:

When three coins are tossed then the outcome will be any one of these combinations. (TTT, THT, TTH, THH. HTT, HHT, HTH, HHH).

So, the total number of outcomes is 8.

Now, for exactly two heads, the favorable outcome is (THH, HHT, HTH).

We can say that the total number of favorable outcomes is 3.

Again, from the formula

Probability = Number of favorable outcomes/Total number of outcomes

Probability = 3/8

∴ The probability of getting exactly two heads is 3/8.

Calculation

Number of composite number in a dice are  (4 and 6)

⇒ Probabilty of composite number in a dice = 2/6 = 1/3

⇒ Number of prime number in a dice = 2, 3 and 5

⇒ Probability of prime number in a dice = 3/6 = 1/2

∴The probability of getting a composite number on the first roll and a prime number on the second roll = 1/2 × 1/3 = 1/6

GIVEN:

Number of unbiased dice = 2

CONCEPT:

Probability (Event) = Number of favorable outcome / Total outcome

CALCULATION:

No. of ways of rolling a pair of dice = 6 × 6 = 36

Let E = event of getting a sum greater than 5 = {(1, 6), (1, 5), (2, 6),(2, 5), (2, 4), (3, 6), (3, 5), (3, 4), (3, 3), (4, 6), (4, 5), (4, 4), (4, 3), (4, 2), (5, 6), (5, 5),(5, 4), (5, 3), (5, 2), (5, 1), (6, 6), (6, 5), (6, 4), (6, 3), (6, 2), (6,1)}

n(E) = 26

⇒ Required probability = 26/36 = 13/18

⇒ The probability of getting sum greater than 5 = 13/18

GIVEN:

Number of unbiased dice = 2

CONCEPT:

Probability (Event) = 1 - (Number of non favorable outcome / Total outcome)

Probability of getting a sum greater than 5 = 1 - (Probability of getting a sum less than or equal to 5)

CALCULATION:

No. of ways of rolling a pair of dice = 6 × 6 = 36

Let F = event of getting a sum less than or equal to 5 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4,1)}

n(F) = 10

⇒ Required probability = 1 - (10/36) = 1 - (5/18) = 13/18

∴ The probability of getting sum greater than 5 = 13/18

Important Points

When we have a large number of cases like 26 in case of Event (E) then we calculate non-favorable outcome(Compliment event i.e. 1 - favourable event)

Mistake Points

In this question, we have to avoid the cases in which sum of digit is equal to five like{(1, 4),(2, 3),(3, 2),(4,1)}

Additional Information

Probabilities for the two dice