Conditional Probability

Q.

A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only.

The probability that the value of the determinant chosen is positive is

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

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

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

4. None of these

Q. 7. A COIN IS TOSSED UNTIL A HEAD APPEARS OR THE TAIL APPEARS 4 TIMES IN SUCCESSION.FIND THE PROBABILITY DISTRIBUTION OF THE NUMBER OF TOSSES.

Q.

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Q.

A determinant of second order is made with the elements $0$ and $1$.

What is the probability that the determinant is positive?

1. $\frac{7}{12}$

2. $\frac{11}{12}$

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

4. $\frac{15}{16}$

Q. A committee of 5 students is selected at random from a group consisting 10 boys and 5 girls. Given that there is at least one girl in the committee, calculate the probability that there are exactly 2 girls in the committee.

1. $\frac{400}{917}$
2. $\frac{400}{1001}$
3. $\frac{143}{143}$
4. $\frac{400}{991}$

Q. 24. A bag contains 5 white, 7 red, and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

Q. Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting equal numbers on the dice is

1. 0.2
2. 0.1
3. 0.5
4. 0.25

Q. 2. Two persons A and B r standing with 10 other persons on the circumference of a circle. If they stand at random, then find the probability that exactly 3 persons r in between A and B

Q. How many $4$-letter code can be formed using the first $10$ letters of the English alphabet, if no letter can be repeated?

Q.

A box contains 15 red marbles, 15 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that atleast one will be green?

1. 

2. 

3. 1

4. 0

Q.

Is conditional probability dependent or independent?

Q.

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A \cap B) = 0.35.
Find
(i) $P(A\cap B)$ (ii) P $(A^{\prime }\cap B^{\prime })$ (iii) P $(A\cap B^{\prime })$
(iv) P $(A\cap B^{\prime })$

Q. 26. What is the probability that the sum of any 2 different single digit natural numbers is a prime number ? (A) 5/24 (B) 13/24 (C) 1/4 (D) none of these

Q. A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?

Q. A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card will be a club or a king?

1. $\frac{1}{13}$
2. $\frac{3}{13}$
3. $\frac{1}{4}$
4. $\frac{4}{13}$

Q. 37. What is the difference between probability of At least & at most of an event.

Q. A hunter's chance of shooting an animal at a distance $r$ is $\frac{a^2}{r^2}(r>a).$ He fires when $r=2a$ if he misses he reloads fires when $r=3a,4a,\cdots$. If he misses at a distance $na$, the animal escapes, then the odds against the hunter is
​​​​​​​(correct answer + 1, wrong answer - 0.25)

1. $\frac{n+1}{n-1}$
2. $\frac{n-1}{n+1}$
3. $\frac{n-1}{n}$
4. $\frac{n+1}{n}$

Q. 28. Two different dice are tossed together. Find the probability : i) Of getting a doublet ii) Of getting a sum 10, of the numbers on the two dice.

Q. Two fair dice are rolled simultaneously. One of the dice shows four. The probability of other dice showing six, is equal to

1. $\frac{2}{11}$
2. $\frac{1}{18}$
3. $\frac{1}{6}$
4. $\frac{1}{36}$

Q. Let $A$ and $B$ be two non-null events such that $A\subset B.$ Then, which of the following statements is always correct?

1. $P\left(A|B\right)=1$
2. $P\left(A|B\right)\le P\left(A\right)$
3. $P\left(A|B\right)\ge P\left(A\right)$
4. $P\left(A|B\right)=P\left(B\right)-P\left(A\right)$

Q. 6. 5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternatively, is?

Q.

A and B are events such that P(A) = 0.42,
P(B) = 0.48 and P(A and B) = 0.16. Determine
(i) P (not A ) (ii) P (not B) and (iii) P (A or B)

Q. 10.A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B i

Q. Let A and B be two events such that
P (A) = 0.5, P (B) = 0.3, and
$P\left(A|B\right)=0.5,$
Then $P\left(A^C|B^C\right)$ equals

1. 0.5
2. 0.6
3. 0.15
4. 0.3

Q. If $15$ boys are randomly divided into $3$ groups of $4,5$ and $6$ boys, the probability that the $3$ youngest boys are in different groups is

1. $4/91$
2. $24/91$
3. $12/91$
4. $18/91$

Q.

A letter is chosen at random from the word “Permutation�. The probability that letter I not a vowel is:

1. 1/2

2. 1/3

3. 1/4

Q. Probability of occurrence of B, when we know that event A has happened is called probability of A given B.

1. True
2. False

Q. Mohan posts a letter to Sohan. It is known that one letter out of $10$ letters does not reach its destination. It is certain that Sohan will reply if he receives the letter. If $A$ denotes the event that Sohan receives the letter and $B$ denotes the event that Mohan gets a reply, then

1. $P\left(B\right)=\frac{81}{100}$
2. $P(A\cap B)=\frac{81}{100}$
3. $P\left(A|\overline{B}\right)=\frac{9}{19}$
4. $P(A\cup B)=\frac{9}{10}$

Q. One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

Q. A bag contains four tickets numbered 00, 01, 10, 11. Four tickets are chosen at random with replacement, the probability that sum of the numbers on the tickets is 23, is

1. $\frac{3}{32}$
2. $\frac{1}{64}$
3. $\frac{5}{256}$
4. $\frac{7}{256}$