Event

Q.

The set of all possible outcomes of a random experiment is called the …… associated with the experiment.

1. Sample space

2. Outcomes

3. Event

4. Experiment

Q.

Box I contain three cards bearing numbers 1, 2, 3; box II contains five cards bearing numbers 1, 2, 3, 4, 5; and box III contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{th}$ box $i=1,2,3.$

The probability that $x_1+x_2+x_3$ is odd, is ?

1. $\frac{29}{105}$

2. $\frac{53}{105}$

3. $\frac{57}{105}$

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

Q.

A possible result of a random experiment is called its ……

1. Favorable outcomes

2. Experiment

3. Outcome

4. Event

Q. 18. The probability that the length of a randomly chosen chord of a circle lies between 2/3 and 5/6 of its diameter is _

Q.

Three numbers are chosen at random without replacement from {1, 2, ......, 15}. Let $E_1$ be the event that minimum of the chosen numbers is 5 and $E_2$ be that their maximum is 10 then

1. $P\left(E_1\right)=\frac{9}{91}$
   

2. $P\left(E_2\right)=\frac{36}{455}$
   

3. $P(E_1\cap E_2)=\frac{4}{455}$
   

4. $P\left(E_1/E_2\right)=\frac{1}{9}$

Q. 14.There are (n-1) red balls, n green balls and(n+1)blue balls, in a bag. The number of ways of choosing two balls from the bag that have different colours is 299.what is the value of n?

Q. 5 whole numbers are randomly chosen and multiplied . Then find : a) probability that last digit is 5 . b) probability that last digit is 0

Q.

A box has 7 red and 4 blue balls. Two balls are drawn at random with replacement and an event is defined as '2 red balls are drawn. Find number of favorable outcomes.

Q. A/an is a subset of the in a random experiment.

1. event
2. sample space
3. probability
4. certainity

Q. The number lock of a suitcase has $4$ wheels each labelled with ten digits i.e. from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

Q. 15. Two dice are thrown simultaneously, find the probability of : (i) 3 not coming up oneither time. (ii) 3 not coming up atleast once, (ii) 3 coming up both times.

Q.

In probability, the event ‘A or B’ can be associated with set :

1. (A - B)’

2. A U B

3. A - B

4. A B

Q.

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 points for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$, respectively, after two games.

$P(X>Y)$ is

1. $\frac{5}{12}$

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

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

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

Q.

Events E and F are such that P(not E or Not F) = 0.25 state whether E and F are mutually exclusive.

Q. In how many ways, three persons each throwing a single dice onces makes a sum of 15.

Q. Let E denote the event "India scores less than 300 in a cricket match". The number of elements in the sample space that favours E is

1. 30
2. 150
3. 300
4. 200

Q. If $4$-digit numbers greater than $5,000$ are randomly formed from the digits $0,1,3,5$ and $7$. What is the probability of forming a number divisible by $5$ when (i) the digits are repeated (ii) the repetition of digits is not allowed?

Q. The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is $\frac{1}{4}$. The probability of selecting a white marble at random from the same jar is $\frac{1}{3}$. If this jar contains $10$ yellow marbles. What is the total number of marbles in the jar?

1. $20$
2. $24$
3. $35$
4. $40$

Q.

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 points for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$, respectively, after two games.

$P(X=Y)$ is

1. $\frac{11}{36}$

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

3. $\frac{13}{36}$

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

Q.

Box I contain three cards bearing numbers 1, 2, 3; box II contains five cards bearing numbers 1, 2, 3, 4, 5; and box III contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{th}$ box $i=1,2,3.$

The probability that $x_1,x_2$ and $x_3$ are in arithmetic progression, is ?

1. $\frac{9}{105}$

2. $\frac{10}{105}$

3. $\frac{11}{105}$

4. $\frac{7}{105}$

Q.

Let E denotes the event "India scores less than 300” in a cricket match between India and South Africa. How many elements are there in the sample space which will favor the event E?

Q. What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?

Q.

While throwing a pair of dice, an event A is defined as 'sum of faces will be at least 10'. Find the total number of favorable outcomes.

Q.

Any subset of an event is called sample space

1. True

2. False

Q. In a random experiment, we can have outcome(s).

1. exactly one
2. more than one
3. no

Q. What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?

Q. Explain in detail the no of ways to select four cards from a well shuffled deck such that : A. Exactly one pair is drawn and the other two cards are different B. 2 different pairs are drawn

Q. List all events associated with the random experiment of tossing of two coins. How many of them are elementary events.