Axiomatic Approach

Q.

What does Intersection mean in probability?

Q. A bag contains $6$ red balls, $8$ white balls, $5$ green balls and $2$ black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is
$\left(i\right)$ White
$\left(ii\right)$ Red or black
$\left(iii\right)$ Not green
$\left(iv\right)$ Neither white nor black

1. $\left(i\right)\frac{1}{11}\left(ii\right)\frac{7}{22}\left(iii\right)\frac{13}{22}\left(iv\right)\frac{1}{4}$
2. $\left(i\right)\frac{4}{11}\left(ii\right)\frac{9}{22}\left(iii\right)\frac{17}{22}\left(iv\right)\frac{1}{2}$
3. None of these
4. $\left(i\right)\frac{5}{11}\left(ii\right)\frac{13}{22}\left(iii\right)\frac{19}{22}\left(iv\right)\frac{1}{7}$

Q. $\left(A\right)$ A box contains $3$ blue, $2$ white and $4$ red marbles. If a marble is drawn from the box. What is the probability that it will be
$\left(i\right)$ White $\left(ii\right)$ Blue $\left(iii\right)$ Red?
$\left(B\right)$ A bag contains $5$ red, $8$ green and $7$ white balls. One ball is drawn at random from the bag, find the probability of getting
$\left(i\right)$ A white ball or a green ball
$\left(ii\right)$ Neither a green ball nor a red ball.

1. $\left(A\right)\left(i\right)\frac{1}{9}\left(ii\right)\frac{2}{3}\left(iii\right)\frac{5}{9}\left(B\right)\left(i\right)\frac{6}{13}\left(ii\right)\frac{11}{20}$
2. $\left(A\right)\left(i\right)\frac{5}{9}\left(ii\right)\frac{1}{4}\left(iii\right)\frac{2}{11}\left(B\right)\left(i\right)\frac{1}{2}\left(ii\right)\frac{5}{19}$
3. $\left(A\right)\left(i\right)\frac{2}{9}\left(ii\right)\frac{1}{3}\left(iii\right)\frac{4}{9}\left(B\right)\left(i\right)\frac{3}{4}\left(ii\right)\frac{7}{20}$
4. None of these

Q. In a box, there are $8$ red, $7$ blue and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

1. $\frac{1}{3}$
2. $\frac{3}{4}$
3. $\frac{7}{19}$
4. $\frac{8}{21}$
5. $\frac{9}{21}$

Q. The probability that at least one of the events A and B occurs is 0.6. If A and B occurs simultaneously with probability 0.2, then $P\left(\overline{A}\right)+P\left(\overline{B}\right)$ is equal to

1. 0.4
2. 0.8
3. 1.2
4. 1.4

Q.

From a well shuffled deck of cards, $2$ cards are drawn with replacement. If $x$ represent numbers of times ace coming, then value of $P(x=1)+P(x=2)$ is

1. $\frac{25}{169}$

2. $\frac{24}{169}$

3. $\frac{49}{169}$

4. $\frac{23}{169}$

Q. $60$ percent people in a group of $10$ people, have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes?

1. $0.13$
2. $0.18$
3. $0.25$
4. $0.36$

Q. For the three events A, B and C, P(exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) $=p^2$, where 0 < p < $\frac{1}{2}$. Then, the probability of at least one of the three events A, B and C occurring is

1. $\frac{3p+2p^2}{2}$
2. $\frac{p+3p^2}{4}$
3. $\frac{3p+2p^2}{4}$
4. $\frac{p+3p^2}{2}$

Q. Fifteen persons, among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

1. $1/7$
2. $2/17$
3. $3/17$
4. $4/17$

Q. $A$'s skill is to $B$ as $1:3$, to $C$'s as $3:2$ and to $D$'s as $4:3$; find the chance that $A$ in three trials one with each person will succeed twice at least.

1. $\frac{11}{28}$
2. $\frac{26}{35}$
3. $\frac{9}{35}$
4. $\frac{13}{28}$

Q. Two events $X$ and $Y$ are occuring simultaneously. Probability of occurance of event $X$ is $0.64$ and that of event $Y$ when event $X$ has already occured is $0.32$. What will be the probability of occurance of events $X$ and $Y$ simultaneously?

1. $0.2048$
2. $0.2400$
3. $0.6400$
4. $0.3200$

Q. Probability of trains A, B and C arriving on times is 1/3, 2/5 and 2/3 respectively. What is the probability that almost one of the trains arrive on time?

a) 7/15 b) 22/45 c) 23/45 d) None of these

Q. From the position given above, all move in the clockwise direction along 3/8 of a circle. Then which of the following is correct at the new position?

1. D is to the north of B
2. A is to the south-east of C
3. C is to the east of D
4. C and D are to east of B
5. None of these

Q. An insurance company selected $1600$ drivers in a particular city to find the relationship between age and number of accidents. The data obtained are given in the following table. Find the probabilities of the following events for a driver chosen at random from the city.
(i) being $25-40$ years of age and having more than $2$ accidents in one year.
(ii) being above $40$ years of age and having accidents more than 1 but less than $3$ in one year.
(iii) having no accidents in one year.
(iv) being below $25$ years of age and having at most $2$ accidents in one year.

Q. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one in a random order till both the faulty machines are identified. Then the probability that only two tests will be required is-

1. $1/2$
2. $1/4$
3. $1/3$
4. $1/6$

Q. In a group of school children 3 individual qualities ( honesty, kindness, patience)are found. The probability of selecting a honest child and probability of selecting a kind child are 4/15 And 2/5 respectively. All of them are likely to be selected. If the number of patient child is 10 what is the total number of children in that group?

Q. A bag contains $3$ red balls, $5$ black balls and $4$ white balls. A ball is drawn at random from the bag. The probability that the ball drawn is black is $\frac{5}{12}$.

Q. Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If $P\left(T\right)$ denotes the probability of occurrence of the event $T$, then

1. $P\left(E\right)=\frac{4}{5}$ , $P\left(F\right)=\frac{3}{5}$
2. $P\left(E\right)=\frac{1}{5},P\left(F\right)=\frac{2}{5}$
3. $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{4}{5}$
4. $P\left(E\right)=\frac{2}{5}$ , $P\left(F\right)=\frac{1}{5}$

Q. Let X and Y be two events such that $P\left(X\right)=\frac{1}{3},P\left(X|Y\right)=\frac{1}{2}$ and $P\left(Y|X\right)=\frac{2}{5}$. Then ?

1. $P\left(Y\right)=\frac{4}{15}$
2. $P\left(\frac{X^{\prime }}{Y}\right)=\frac{1}{2}$
3. $P(X\cup Y)=\frac{2}{5}$
4. $P(X\cap Y)=\frac{1}{5}$