Probability Test

Result

Probability Test - 6

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

In a collection of 6 English books and 4 Reasoning books, the probability that 3 particular English books will be lying together is

A

B

C

D
None of these

Solution

Number of ways of 3 particular English books will be lying together = 8! x 3!

Total number of ways = (6 + 4)! = 10!

Required probability =
Question 2
1 / -0

You are given a box with 25 cards in it. 10 of these cards have letter "I" printed on them and the other 15 have the letter "T" printed on them. If you pick up 3 cards one by one at random and keep them in the same order, the probability of making the word I.I.T. is

A

B

C

D

Solution

Required Probability,
P('I' first Draw)+P('I' first Draw) + P('T' first Draw)
= [10C1]/[25C1] + [9C1]/[24C1] + [15C1]/[23C1]
=[10/25] × [9/24] × [15/23]
= 1350/13800
= 45/460
= 9/92
Question 3
1 / -0

N students have to stand in a row. If all possible permutations are equally likely, the probability of two particular students standing side by side is

A

B

C

D

Solution

n (S) = number of ways of arranging N students in a row = ^NP_N = N!
Consider two particular students as one.
Then (N – 1) students can be arranged in (N – 1)! ways and these two students can be arranged amongst
themselves in 2! ways.
n (E) = (N – 1)! ´ 2!
Hence, required probability =
Question 4
1 / -0

The odds against an event A are 5 : 3 and odds in favour of another independent event B are 7 : 5. The chances that neither A nor B occurs is

A

B

C

D

Solution

The odds against an event A are 5 : 3.
So, Probability of occurence if event A =

And odds in favour of another independent event B are 7 : 5.
So, Probability of occurence if event B =

The chances that neither A nor B occurs is =
Question 5
1 / -0

A bag contains 6 white and 4 black balls. A man pulls out 2 balls at random. The probability that they are of the different colour is

A

B

C

D
None of these

Solution

n (S) = number of ways of pulling 2 balls out of 10
= ¹⁰C₂ = = 45.
n (E) = (number of ways of pulling 2 balls out of 6 or 2 balls out of 4)
= (⁶C₁ x ⁴C₁) = (6 x 4) = 24.
Required probability = =
Question 6
1 / -0

A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in the first two draws is

A

B

C

D

Solution

Required probability =
Question 7
1 / -0

The probability of getting a sum of more than 7 when a pair of dice is thrown, is

A

B

C

D
None of these

Solution

Favourable Cases = (2, 6) (3, 5) (3, 6) (4, 4) (4, 5) (4, 6) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 2) (6, 3) (6, 4) (6, 5) (6, 6) = 15 in total
Required probability = = .
Question 8
1 / -0

From each of two married couples, one of the partners is selected randomly. The probability that those selected are of the opposite sex is

A

B

C

D

Solution

number of favourable outcomes/ total number of outcomes
= ½
Question 9
1 / -0

A bag contains 15 white and 4 green balls. One ball is drawn at random. The probability that it is green is

A

B

C

D

Solution

Total number of balls = 15 + 4 = 19
Number of green balls = 4
Required probability =
Question 10
1 / -0

Two fair dice are thrown. Let X be the event that the first die shows an even number and Y be the event that the second die shows an odd number. The two events X and Y are

A
mutually exclusive

B
independent and mutually exclusive

C
dependent

D
independent

Solution

Events are independent but mutually exclusive as the outcomes of both events are different.
Question 11
1 / -0

The probability of having 53 Mondays in a year is

A

B

C

D
None of these

Solution

Normal year has 365 days.
365/7 = 52, remainder = 1
52 weeks are there 52 Sundays, 1 day extra;
For 53 Sundays this day should be a Sunday. So, P (53 Sundays) = 1/7.
Question 12
1 / -0

The probability that A can solve a problem is 1/3, and the probability that B can solve the problem is 1/4. The probability that at least one of A and B will be able to solve the problem is

A

B

C

D

Solution
Question 13
1 / -0

Two cards are drawn from a pack. The probability of getting a king and a queen is

A

B

C

D
None of these

Solution

Probability of getting a king and a queen = (K Q) (Q K) = P(KQ) + P(QK)
= =
Question 14
1 / -0

A husband and wife appear for an interview for the same post. The probability of husband's selection is and that of wife's is . What is the probability that none of them will be selected?

A

B

C

D
None of these

Solution

The probability of husband's selection is .

The probability of wife selection is .

The required probability =
= =
Question 15
1 / -0

There are 40 cards with numbers 1 to 40 printed on them. What is the probability of finding a card with a multiple of 4 in a draw?

A

B
1

C

D

Solution

Total number of possible outcomes = 40

Favourable outcomes = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 = 10

So, the required probability = ^.
Question 16
1 / -0

The chances of a win of two race horses are and respectively. What is the probability that at least one will win when the horses are running in different races?

A

B

C

D
None of these

Solution
Question 17
1 / -0

Four letters are written to different persons and addresses on the envelopes are also written. Without looking at the addresses, the probability that letters go into right envelopes is

A

B

C

D

Solution

There are four letters and four directed envelopes.
Therefore, they can be put into the envelopes in ⁴C₄= 4 ! = 624 ways, out of which only one is correct.
Thus, the required probability = 1/24
Question 18
1 / -0

A work is given to 4 men and their probabilities for doing the work are , , and respectively. The probability that the work done is

A

B

C

D
None of these
Question 19
1 / -0

Ram and Ravana throw a dice. The chance that both Ram and Ravana throw the same number is

A

B

C

D
None of these

Solution

Required probability = 6/36 = 1/6.
Question 20
1 / -0

If A and B are two events such that
(i) P(A B) = , P(B A) = .
(ii) P(A) = , then the events A and B are

A
independent

B
dependent

C
mutually exclusive

D
none of these

Solution

As, Occurance of A does not affect the probability of B occurring. So, two events, A and B, are independent.