# Conditional Probability

## Trending Questions

**Q.**

A contest consists of predicting the results of the win, draw or defeat of $7$ football matches. A sent his entry by predicting at random. The probability that his entry will contain exactly $4$ correct predictions is

$\frac{8}{{3}^{7}}$

$\frac{16}{{3}^{7}}$

$\frac{280}{{3}^{7}}$

$\frac{560}{{3}^{7}}$

**Q.**

A bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then the probability for the ball chosen be white is

$\frac{2}{15}$

$\frac{7}{15}$

$\frac{8}{15}$

$\frac{14}{15}$

**Q.**A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour ?

- 4144
- 4039
- 4044
- 4441
- 4439

**Q.**

If $\text{A}$ and $\text{B}$ are two events such that$\text{P(AUB)}$$+$$\text{P(A\u2229B)}$$=$$\frac{7}{8}$, and $\text{P(A)}$$=$$\text{2P(B)}$, then $\text{P(A)}$$=$

$\frac{7}{12}$

$\frac{7}{24}$

$\frac{5}{12}$

$\frac{17}{24}$

**Q.**A box contains 6 blue, 5 green and 4 red balls. If two balls are picked at random, then what is the probability that neither is blue?

- None of these
- 1235
- 1121
- 1021
- 35

**Q.**A Number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

**Q.**

A box contains $100$ bulbs, out of which $10$ are defective. A sample of $5$ bulbs is drawn. The probability that none is defective, is

$\frac{9}{10}$

${\left(\frac{1}{10}\right)}^{5}$

${\left(\frac{9}{10}\right)}^{5}$

${\left(\frac{1}{2}\right)}^{5}$

**Q.**

A bag contains $n$ white and $n$ red balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one red ball is

$\frac{2n}{{}^{2n}C_{n}}$

$\frac{{2}^{n}}{{}^{2n}C_{n}}$

$\frac{1}{{}^{2n}C_{n}}$

None of these

**Q.**

Ten students are seated at random in a row. The probability that two particular students are not seated side by side is

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{1}{5}$

**Q.**

A natural number is chosen at random from amongst the first $300$. What is the probability that the number chosen is a multiple of $2\mathrm{or}3\mathrm{or}5$ ?

$\frac{1}{10}$

$\frac{11}{15}$

$\frac{4}{150}$

$\frac{17}{30}$

**Q.**A box contains 2 blue, 3 green and 5 red balls. If three balls are drawn at random, what is the probability that all balls are different in color?

- 14
- 310
- 37
- 411
- 29

**Q.**

A letter is taken out at random from ‘$ASSISTANT$’ and another is taken out from ‘$STATISTICS$’. The probability that they are the same letters, is

$\frac{1}{45}$

$\frac{13}{90}$

$\frac{19}{90}$

None of these

**Q.**There are 8 brown balls, 4 oragne balls and 5 black balls in a bag. Five balls are chosen at random. What is the probability of there being 2 brown balls, 1 orange ball and 2 black balls?

- 1911547
- 1801547
- 2801547
- 1801547
- None of these

**Q.**

A bag contains 3 white, 5 red and 7 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

3/22

1/91

none

1/22

2/91

**Q.**

For$k=1,2,3$ the box, $Bk$ contains $k$ red balls and $(k+1)$white balls. Let $P\left({B}_{1}\right)=\frac{1}{2},P\left({B}_{2}\right)=\frac{1}{3}$and $P\left({B}_{3}\right)=\frac{1}{6}$.

A box is selected at random and a ball is drawn from it.

If a red ball is drawn, then the probability that it has come from box ${B}_{2}$ is

$\frac{35}{78}$

$\frac{14}{39}$

$\frac{10}{13}$

$\frac{12}{13}$

**Q.**If 3 balls are drawn at random, what is the probability that 1 is green and the other 2 are black ?

- 487
- 285
- 185
- 385
- 585

**Q.**If 5 balls are picked at random, what is the probability that none are orange ?

- 33442
- 44233
- 15167
- 23235
- 35235

**Q.**

Two dice are tossed simultaneously. Then the probability that the total score is a prime number is:

none

5/12

1/2

1/12

7/12

**Q.**

The probability that in a random arrangement of the letters of the word 'ANIMAL', the two A's come together.

none

4/5

2/5

2/3

1/3

**Q.**

A number is selected randomly from the first thirty natural numbers. What are the chances that it is a multiple of either 3 or 13?

13/30

2/5

3/5

17/30

None of these

**Q.**

x1, x2, x3, ..., x40 are forty real numbers such that xr<xr+1for r = 1, 2, 3... 39. Five numbers out of these are picked up at random. The probability that the five numbers have x20 as the middle number is:

19/55

(

^{19}C_{2}×^{20}C_{2})/(^{40}C_{4})(

^{19}C_{2}×^{20}C_{2})/(^{ 40}C_{5})(

^{19}C_{3}×^{20}C_{2})/(^{ 40}C_{4})None of these

**Q.**What is the probability that product of two integers chosen at random has the same unit’s digit as the integers themselves?

**Q.**

An urn contains 6 red, 4 blue and 3 green marbles. If 2 marbles are picked at random, then what is the probability that both the marbles are red?

**Q.**If A and B are two events such that P(A∪B)=56, P(A∩B)=13 and P(¯B)=13, then the value of P(A) is

- 13
- 12
- 14
- 23

**Q.**Arun draws 3 balls at random from a basket which contains 4 red and 5 blue balls. What are the odds in favour of these being all blue?

- 5 : 42
- 5 : 37
- 4 : 43
- 4 : 50

**Q.**10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

- 511
- 711
- 23
- 811