Probability

Q. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's is 1/5. What is the probability that both of them will be selected?

1. $\frac{2}{7}$
2. $\frac{1}{35}$
3. $\frac{24}{25}$
4. $\frac{11}{35}$

Q. From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being Kings.

1. 1/15
2. 25/57
3. 35/256
4. None of these

Q.

Two fair dice, each with faces numbered$1,2,3,4,5$ and $6$, led together and the sum of the numbers on the faces is observed.

This process is repeated till the sum is either a prime number or a perfect square.

Suppose the sum turns out to be a perfect square before it turns out to be a prime number.

If $p$is the probability that this perfect square is an odd number, then the value of $14p$ is _____

Q. A card is drawn from an ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?

1. 9 : 4
2. 4 : 9
3. 5 : 9
4. 9 : 5

Q.

A number is chosen at random among the first $120$ natural numbers. The probability of the number chosen to be a multiple of $5$ or $15$ is:

1. $\frac{1}{5}$

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

3. $\frac{1}{24}$

4. $\frac{1}{6}$

Q. If a card is picked up at random from a pack of 52 cards. Find the probability that it is 'a spade' or 'a king' or 'a queen'

1. $\frac{21}{52}$
2. $\frac{5}{13}$
3. $\frac{19}{52}$
4. None of these

Q. A bag contains 3 red, 6 white and 7 black. Two balls are drawn at random. Probability that both are black?

1. $\frac{1}{8}$
2. $\frac{7}{40}$
3. $\frac{12}{40}$
4. $\frac{13}{40}$

Q. A bag contains four black and five red balls. If three balls from the bag are chosen at random, what is the chance that they are all black?

1. $\frac{1}{21}$
2. $\frac{1}{20}$
3. $\frac{2}{23}$
4. $\frac{1}{9}$

Q. Two balls are to be drawn from a bag containing 8 grey and 3 blue balls. Find the chance that they will both be blue.

1. $\frac{1}{5}$
2. $\frac{3}{55}$
3. $\frac{11}{15}$
4. $\frac{14}{45}$

Q. An event is :

1. The terminals of an activity
2. A definite time interval
3. A definite position of an activity
4. A defined job

Q.

If four dice are thrown together, the probability that the sum of the number appearing on them is 13 is

1. $\frac{35}{324}$

2. $\frac{5}{216}$

3. $\frac{11}{216}$

4. $\frac{11}{432}$

Q. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's is 1/5. What is the probability that none of them will be selected?

1. $\frac{2}{7}$
2. $\frac{1}{35}$
3. $\frac{24}{35}$
4. $\frac{11}{35}$

Q. $\text{A signal}x\left(t\right)=e^{-t}u\left(t\right)\text{is passed through an ideal low pass filter with cut-off frequency of}{\omega }_c\text{rad/sec, then the value of}{\omega }_c\text{for the output energy of low pass filter is 90\% of the}\text{input energy will be \_\_\_\_\_\_\_\_rad/sec}$

1. 6.314

Q. A bag contains 3 green and 7 white balls. Two are drawn from the bag in succession with replacement. What is the probability that both white?

1. $\frac{1}{7}$
2. $\frac{5}{11}$
3. $\frac{7}{11}$
4. $\frac{7}{15}$

Q. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is ______.

1. 
   0.6976
2. 
   0.3024
3. 
   0.4235
4. 
   0.8125

Q. In throwing a fair dice, what is the probability of getting the number '3'?

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{1}{9}$
4. $\frac{1}{12}$

Q. You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

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

Q. The probability distribution of monthly sale of a certain item is as follows:

$\begin{array}{ccccccccc}\text{Monthly sales (units)}& 1& 2& 3& 4& 5& 6& 7& 8\\ \text{Probability}& 0.06& 0.08& 0.13& 0.19& 0.26& 0.13& 0.08& 0.07\end{array}$

The carrying cost of inventory is Rs. 50 per unit per month and the shortage cost is Rs. 84 per unit per month. What will be the optimum stock level ?

1. 4.57 units
2. 4 units
3. May be (a) or (c)
4. 5 units

Q. Find the chance of throwing at least one ace in a simple throw with two dice.

1. $\frac{1}{12}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{11}{36}$

Q. Two fair coins are tossed. Find the probability of obtaining 1 Head and 1 Tail

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

Q. $AandBaremutuallyexclusiveeventsofanexperiment.$
$IfP\left(\overline{A}\right)=0.65,P(A\cup B)=0.65andP\left(B\right)=P.$
$FindthevalueofP.$

1. 0.70
2. 0.30
3. 0.63
4. 0.35

Q. Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?

1. 17/24
2. 3/8
3. 1/2
4. 5/8

Q. What is the probability that a leap year, selected at random, will contain 53 Saturdays?

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

Q. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's is 1/5. What is the probability that only one of them will be selected?

1. $\frac{2}{7}$
2. $\frac{1}{35}$
3. $\frac{24}{25}$
4. $\frac{11}{35}$

Q. An urn contains 25 balls numbered 1 to 25. Suppose getting an odd numbered ball is considered a 'success'. If two balls are drawn from the urn with replacement.
Find the probability of getting two successes.

1. $\frac{169}{625}$
2. $\frac{312}{626}$
3. $\frac{481}{626}$
4. $\frac{144}{625}$

Q. If the probability that A will live 15 years is 7/8 and that B will live 15 years is 9/10, then what is the probability that both will live after 15 years?

1. $\frac{1}{20}$
2. $\frac{63}{80}$
3. $\frac{1}{5}$
4. None of these

Q. If a card is picked up at random from a pack of 52 cards. Find the probability that it is a king or queen.

1. $\frac{3}{13}$
2. $\frac{2}{13}$
3. $\frac{7}{52}$
4. $\frac{1}{169}$

Q. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is

1. 
   $\frac{1}{8}$
2. 
   $\frac{1}{36}$
3. 
   $\frac{1}{4}$
4. 
   $\frac{1}{12}$

Q. The probability that a k-digit number does NOT contain the digits 0, 5 or 9 is

1. 
   ${0.3}^k$
2. 
   ${0.6}^k$
3. 
   ${0.7}^k$
4. 
   ${0.9}^k$

Q. The probabilities that a student will receive an A, B, C or D grade are 0.30, 0.38, 0.22 and 0.01, respectively. What is the probability that the student will receive at least B grade?

1. 0.38
2. 0.42
3. 0.68
4. None of these