Conditional Probability

Q. A single dice is thrown twice. What is the probability that the sum is neither 8 nor 9?

1. 1/9
2. 5/36
3. 1/4
4. 3/4

Q. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

1. $\frac{1}{8}$
2. $\frac{1}{2}$
3. $\frac{3}{8}$
4. $\frac{3}{4}$

Q. An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is

1. 0.5
2. 0.18
3. 0.12
4. 0.06

Q. A and B friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

1. $\frac{1}{4}$
2. $\frac{1}{16}$
3. $\frac{7}{16}$
4. $\frac{9}{16}$

Q.

What is the normalization factor?

Q.

A card is drawn from a well shuffled deck of $52$ cards. find the probability of getting a king of red colour.

Q. Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is

1. $\frac{5}{11}$
2. $\frac{1}{2}$
3. $\frac{7}{13}$
4. $\frac{6}{11}$

Q. The probability that two friends share the same birth-month is:

1. $\frac{1}{6}$
2. $\frac{1}{12}$
3. $\frac{1}{144}$
4. $\frac{1}{24}$

Q. A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

1. ${\left(\frac{1}{2}\right)}^2$
2. ${}^{10}{C}_2{\left(\frac{1}{2}\right)}^2$
3. ${\left(\frac{1}{2}\right)}^{10}$
4. ${}^{10}{C}_2{\left(\frac{1}{2}\right)}^{10}$

Q.

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number on the faces showing up is (up to third decimal place)

1. 0.0278

Q. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

1. 1/3
2. 1/2
3. 2/3
4. 3/4

Q.

An ordinary dice is rolled for a certain number of times.

If the probability of getting an odd number $2$ times is equal to the probability of getting an even number $3$ times, then the probability of getting an odd number for odd number of times is:

1. $\frac{3}{16}$

2. $\frac{1}{2}$

3. $\frac{5}{16}$

4. $\frac{1}{32}$

Q. A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is

1. 1/3
2. 3/7
3. 1/2
4. 4/7

Q. There are 3 red socks, 4 green socks and 3 blue socks, you choose 2 socks. The probability that they are of the same colour is

1. 1/5
2. 7/30
3. 1/4
4. 4/15

Q. A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is

1. 2/315
2. 1/630
3. 1/1260
4. 1/2520

Q. The box 1 contains chips numbered 3, 6, 9, 12 and 15. The box 2 contains chips numbered 11, 6, 16, 21 and 26. Two chips, one from each box are drawn at random.

The number written on these chips are multiplied. The probability for the product to be an even number is

1. $\frac{6}{25}$
2. $\frac{2}{5}$
3. $\frac{3}{5}$
4. $\frac{19}{25}$

Q. Aishwarya studies either Computer Science or Mathematics everyday. If she studies Computer Science on a day, then the probability that she studies Mathematics on the next day is 0.6. If she studies Mathematics on a day, then the probability that she studies Computer Science on the next day is 0.4. Given that Aishwarya studies Computer Science on Monday, what is the probability that she studies Computer Science on Wednesday?

1. 0.24
2. 0.36
3. 0.4
4. 0.6

Q. A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is

1. $\frac{1}{90}$
2. $\frac{1}{2}$
3. $\frac{19}{90}$
4. $\frac{2}{9}$

Q.

Cancidates were asked to come to an interview with 3 pens each. Black, Blue, greena nd red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is .

1. 0.2

Q. The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

1. 0.181
2. 0.191
3. 0.222
4. 0.826

Q. A person on a trip has a choice between private car and public tarnsport. The probability of using a private car is 0.45. While using the public transport further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro respectively would be

1. 0.45, 0.30 and 0.25
2. 0.45, 0.25 and 0.30
3. 0.45, 0.55 and 0.00
4. 0.45, 0.35 and 0.20

Q. A fair coin is tossed n times. The probability that the difference between the number of heads and tails in (n - 3) is

1. $2^{-n}$
2. 0
3. ${}^n{C}_{n-3}{2}^{-n}$
4. $2^{-n+3}$

Q.

The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is (round off to two decimal places).

1. 0.17

Q. The chance of a student passing an exam is 20%. The chance of student passing the exam and getting above 90% marks in it is 5%. Give that a student passes the examination, the probability that the student gets above 90% marks is

1. $\frac{1}{18}$
2. $\frac{1}{4}$
3. $\frac{2}{9}$
4. $\frac{5}{18}$

Q. An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

1. $\frac{1}{32}$
2. $\frac{13}{32}$
3. $\frac{16}{32}$
4. $\frac{31}{32}$

Q.

Let there be three independent events $E_1,E_2\&E_3$. The probability that only $E_1$ occurs is $\alpha$, only $E_2$ occurs is $\beta$ and only $E_3$ occurs is $\gamma$ . Let ‘$p$’ denote the probability of none of the events that occur that satisfies the equations $(ɑ–2\beta )p=ɑ\beta$ and $(\beta –3\gamma )p=2\beta \gamma$ . All the given probabilities are assumed to lie in the interval $(0,1)$Then , $\frac{[\text{probability of occurrence of}{E}_1]}{[\text{probability of occurrence of}{E}_3]}$is equal to ___

Q. An unbalanced dice (with six faces numbered 1 to 6) is thrown. The probability that face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is same. If the probability that the face is even, given that it is greater than 3 is 0.75, then the probability that the face value exceeds 3 is .

1. 0.468

Q.

The expected number of failures preceding the first success in an infinite series of independent trials with constant probability $p$ is

Q. An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

1. $\frac{65}{156}$
2. $\frac{67}{156}$
3. $\frac{79}{156}$
4. $\frac{89}{156}$

Q. Parcels from sender S receiver R pass sequentially through two post-offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is .

1. 0.444