Probability Test

Result

Probability Test - 27

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
4 / -1

Three numbers are chosen at random without replacement from {1, 2, ...8}. The probability that their minimum is 3, given that their maximum is 6, is

A
3/8

B
1/5

C
1/2

D
2/3

Solution
Question 2
4 / -1

Let U₁ and U₂, be two urns such that U₁ contains 3 white and 2 red balls and U₂, contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears, then 2 balls are drawn at random from U₁ and put into U₂. Now, 1 ball is drawn at random from U₂.
22. The probability of the drawn ball from U₂ being white

A
13/30

B
23/30

C
19/30

D
11/30
Question 3
4 / -1

Let U₁ and U₂, be two urns such that U₁ contains 3 white and 2 red balls and U₂, contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears, then 2 balls are drawn at random from U₁ and put into U₂. Now, 1 ball is drawn at random from U₂.
If the drawn ball from U₂ is white, then the probability that head appeared on the coin is

A
17/23

B
11/23

C
15/23

D
12/23

Solution
Question 4
4 / -1

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then

A
P(E) = 4/5, P(F) = 3/5

B
P(E) = 1/5, P(F) = 2/5

C
P(E) = 2/5, P(F) = 1/5

D
P(E) = 3/5, P(F) = 4/5

Solution
Question 5
4 / -1

If A, B and C are pairwise independent events with P(C) > 0 and P(A ∩ B ∩ C) = 0. Then, P(A^c ∩ B^c ∕ C) is equal to

A
P(A^c) - P(B)

B
P(A) - P(B^c)

C
P(A^c) + P(B^c)

D
P(A^c) - P(B^c)
Question 6
4 / -1

If A and B are two non-empty sets with B^c denoting the complement of set B such that B ⊂ A, then which of the following probability statements hold correct?

A
P(A ∩ B^c) = P(B) - P(A)

B
P(A ∩ B^c) = P(A) - P(B)

C
P(B) ≤ P(A)

D
P(A) ≤ P(B)
Question 7
4 / -1

A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal green is

A
3/5

B
6/7

C
20/23

D
9/20

Solution
Question 8
4 / -1

Two dice are tossed once. The probability of getting even number at the first die or a total of 8 is

A
1/36

B
3/36

C
11/36

D
5/9

Solution
Question 9
4 / -1

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ..., 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero equals

A
1/14

B
1/7

C
5/14

D
1/50

Solution
Question 10
4 / -1

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed, is

A
1/2

B
2/5

C
1/5

D
2/3

Solution