4
Q:

Two dice are rolled simultaneously. Find the probability of getting a total of 9.

A) 1/3 B) 1/9
C) 8/9 D) 9/10

Answer:   B) 1/9



Explanation:

S = { (1, 1), (1, 2), (1, 3), (1, 4),(1, 5), (1, 6), (2, 1), (2, 2),.........(6, 5), (6, 6) }

=> n(S) = 6 x 6 = 36

E = {(6, 3), (5, 4), (4, 5), (3, 6) }

=> n(E) = 4

Therefore, P(E) = 4/36 = 1/9

Q:

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?

A) 1/7 B) 8!
C) 7! D) 1/14
 
Answer & Explanation Answer: D) 1/14

Explanation:

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14. 

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8 410
Q:

A fair six-sided die is rolled twice. What is the probability of getting 4 on the first roll and not getting 6 on the second roll ?

A) 1/36 B) 5/36
C) 1/12 D) 1/9
 
Answer & Explanation Answer: B) 5/36

Explanation:

The two events mentioned are independent.

The first roll of the die is independent of the second roll. Therefore the probabilities can be directly multiplied.

P(getting first 4) = 1/6

P(no second 6) = 5/6

Therefore P(getting first 4 and no second 6) = 1/6 x 5/6 = 5/36

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2 272
Q:

Let K and L be events on the same sample space, with P (K) = 0.8 and P (B) = 0.6. Are these two events are disjoint ?

A) TRUE B) FALSE
Answer & Explanation Answer: B) FALSE

Explanation:

These two events cannot be disjoint because P(K) + P(L) > 1.


P(AꓴB) = P(A) + P(B) - P(AꓵB).


An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4


And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

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1 212
Q:

What is the probability that a leap year has 53 Saturdays and 52 Sundays ?

A) 1/7 B) 2/7
C) 1/2 D) 3/2
 
Answer & Explanation Answer: A) 1/7

Explanation:

A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Friday, Saturday}

Required Probability = 1/7

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10 658
Q:

Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is  ?

A) 16/19 B) 1
C) 3/2 D) 17/20
 
Answer & Explanation Answer: D) 17/20

Explanation:

n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(E U P) = 10/20 + 8/20 - 1/20 = 17/20

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5 614