Probability

Q.

Prove that $\frac{1}{0}=$infinity

Q.

A bag contains $3$ red, $4$ white and $5$ black balls. Three balls are drawn at random. The probability of being their different colors is

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

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

3. $\frac{8}{11}$

4. none of these

Q.

What is the probability of getting a multiple of $3$ when a die is tossed?

Q.

A coin is tossed once, what is the probability of getting a head?

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

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

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

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

Q.

The probability of happening and event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$are mutually exclusive events, then the probability of happening neither $A$ nor $B$ is

1. $0.6$

2. $0.2$

3. $0.21$

4. None of these

Q.

In tossing of 3 coins, the probability of getting exactly 1 head is:

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

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

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

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

Q.

A card is drawn from a pack of cards. Find the probability that the card will be queen or a heart

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

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

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

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

Q.

The probability that a non-leap year has $53$ Sundays is

1. $\frac{2}{7}$

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

3. $\frac{3}{7}$

4. None of these

Q.

Which of the following arguments are correct and which are not correct? Give reasons for your Solution:

1. If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails, or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.

2. If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$

Q.

Let $A$ and $B$ be two independent events. The probability that both $A$ and $B$ occur together is $\frac{1}{6}$ and the probability that either of them occurs is$\frac{1}{3}$. The probability of occurrence of $A$ is

1. $0\text{or}1$

2. $\frac{1}{2}\text{or}\frac{1}{3}$

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

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

Q.

In a certain town, $40\%$ of the people have brown hair, $25\%$ have brown eyes and$15\%$ have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is

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

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

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

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

Q.

A person draws a card from a pack of playing cards, replaces it, and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail exactly the first two times is

1. $9/64$

2. $1/64$

3. $1/16$

4. $9/16$

Q.

The probability of getting a multiple of 2 when an unbiased die is thrown is $\frac{1}{2}$.

1. True

2. False

Q. The probability of drawing two clubs from a standard 52 card deck is 0.0588. The probability of drawing the first club is 0.25. What is the probability of drawing a second club, given the first card drawn was a club?

Q.

A five digit number is formed by writing the digits $1,2,3,4,5$ in a random order without repetitions. Then, the probability that the number is divisible by $4$ is

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

2. $\frac{18}{5}$

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

4. $\frac{6}{5}$

Q.

Let $X=\{1,2,3,4,5\}$ and $Y=\{1,3,5,7,9\}$. Which of the following is/are relations from $X$ to $Y$?

1. $R_1=\left\{\right(x,y\left)\right|y=2+x,x\in Y,y\in Y\}$

2. $R_2=\{(1,1),(2,1),(3,3),(4,3),(5,5)\}$

3. $R_3=\{(1,1),(1,3),(3,5),(3,7),(5,7)\}$

4. $R_4=\{(1,3),(2,5),(2,4),(7,9)\}$

Q.

A point is selected at random from the interior of the circle. The probability that the point is closer to the centre than the boundary of the circle is

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

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

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

4. None of these

Q.

Two aeroplanes $\text{I}$ and $\text{II}$ bomb a target in succession. The probabilities of $\text{I}$ and $\text{II}$ scoring a hit correctly are $0.3$ and $0.2$, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is

1. $0.06$

2. $0.14$

3. $0.32$

4. $0.7$

Q.

In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at least four successes will be

1. $\frac{496}{729}$

2. $\frac{500}{729}$

3. $\frac{400}{729}$

4. $\frac{600}{729}$

Q.

Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to

1. $\frac{1}{27}$

2. $\frac{1}{9}$

3. $\frac{4}{27}$

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

Q.

An urn contains $3$ red and $5$ blue balls. The probability that two balls are drawn in which 2nd ball drawn is blue without replacement is

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

2. $\frac{5}{56}$

3. $\frac{5}{8}$

4. $\frac{20}{56}$

Q.

A locker can be opened by dialing a fixed three digit code (between $000$ and $999$). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the $kth$ trail is

1. $\frac{k}{999}$

2. $\frac{k}{1000}$

3. $\frac{k-1}{1000}$

4. None of these

Q.

Odds $8$ to $5$against a person who is $40$ years old living till he is $70$ and $4$ to $3$ against another person now $50$ till he will be living $80$. Probability that one of then will be alive next $30$ years

1. $\frac{59}{91}$

2. $\frac{44}{91}$

3. $\frac{51}{91}$

4. $\frac{32}{91}$

Q.

The coefficient of correlation between two variables $x$ and $y$ are $0.8$ while the regression coefficient of $y$ on $x$ is $0.2$. Then the regression coefficient of $x$ on $y$ is

1. $-3.2$

2. $3.2$

3. $4$

4. $0.16$

Q.

A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is

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

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

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

4. None of these.

Q.

A student argues that ‘there are 11 possible outcomes $2,3,4,5,6,7,8,9,10,11and12.$ Therefore, each of them has a probability $\frac{1}{11}$$$\begin{gathered} P(sum10)=\frac{3}{36} \\ E(sum11)=(5,6),and(6,5) \end{gathered}$$

Do you agree with this argument? Justify your Solution.

Q.

If a dice is thrown $5$ times, then the probability of getting $6$ exact three times is

1. $\frac{125}{388}$

2. $\frac{125}{3888}$

3. $\frac{625}{23328}$

4. $\frac{250}{2332}$

Q.

If $P\left(A\right)=P\left(B\right)=x$and $P(A\cap B)=P(A\cap B)=\frac{1}{3}$, then $x$ is equal to

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

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

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

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

Q.

Question 132

In a test, +3 marks are given for every correct answer and - 1 mark is given for every incorrect answer. Sona attempted all the questions and scored +20 marks, though she got 10 correct answers.
How many incorrect answers has she attempted?
How many questions were given in the test?

Q.

A bag $A$ contains $2$ white and $3$ red balls and bag $B$ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $B$ was

1. $\frac{5}{14}$

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

3. $\frac{5}{18}$

4. $\frac{25}{52}$