Simple and Compound Event

Q. Which of the following is/are compound events?

1. An event where compound interest happen

2. An event which has more than one sample point

3. An event combined with another event

4. An event derived from another event

Q.

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

Q. 31.Three persons A, B and C throw a die in succession till one gets a six and wins the game.find their respective probabilities of winning

Q.

Three coins are tossed once. Let A denote the event "three heads show ", B denote the event "two heads and one tail show", c denote the event "three tails show" and D denote the event "a head show on the first coin", Which events are (i) mutually exclusive ? (ii) simple ? (iii) compound?

Q.

Which of the following is/are simple event?

1. While throwing a die an even prime number turns up

2. While throwing a die, an even or odd number turns up

3. In a football match, a draw happens. (when we are considering results of that match)

4. Two heads occur while throwing a coin twice

Q. Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are (i) mutually exclusive? (ii) simple? (iii) compound?

Q. When a single dice is thrown, the occurrence of a/an number is an example of a simple event.

1. prime
2. even
3. composite
4. even prime

Q.

An experiment involves rolling a pair of dice and recording the number that comes up.

Suppose,

A: the sum is greater than 8.
B: 2 occurs on either die.

Then A and B are ....... events.

1. Favorable events

2. Mutually exclusive events

3. Exhaustive events

4. Random experiment

Q. Which of the following events is/are compound event(s)?

1. Two heads are obtained by a coin tossed twice.
2. A die is thrown twice and the sum of the numbers appearing is observed to be 6.
3. Card drawn from a pack of 52 cards is a king.
4. Three coins are tossed simultaneously. Head is obtained on first two coins.

Q.

In a game a person wins a TV if in four throws of a dice he get sum greater than 20 .In three throws he got numbers as 5, 3, 6. What should be his fourth throw so that he wins a TV?

1. 5 or 6

2. 5

3. 6

4. never wins.

Q. If $\frac{(1-3p)}{2},\frac{(1+4p)}{3},\frac{(1+p)}{6}$ are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is
(a) (0, 1)
(b) (−1/4, 1/3)
(c) (0, 1/3)
(d) (0, ∞)

Q.

Two dice are thrown. The events P and Q are as follows:

P: getting an odd number on the first die.
Q: getting the sum of the numbers on the dice less than 5.
Then, P and Q is:

1. 

2. 

3. 

4. 

Q. A die is thrown describe the following events:
(i) A : a number is less than $7$
(ii) B : a number is greater than $7$
(iii) C : a multiple of $3$
(iv) D : a number less than $4$
(v) E : an even number greater than $4$
(vi) F : a number not less than $3$
Also find $A\cup B,A\cap B,B\cup C,E\cap F,D\cap E,A-C,D-E,E\cap F^{\prime },F^{\prime }$

Q. 39. if a coin is tossed twice what is the probability of getting exactly one head

Q. Describe the following events A, B, C in the random experiment of tossing three unbiased coins: A: event of getting three tails B: event of getting one head C: event of getting almost one tail Show that, (i) A is an elementary event while B & C are compound events. (ii)Events A, B & C are manually exclusive and exhaustive events.

Q. Given two mutually exclusive events A and B such that P(A) = 1/2 and P(B) = 1/3, find P (A or B).

Q.

Which of the following is/are the definition of a simple event?

1. An event which is simple to understand

2. An event which will has simple outcomes

3. An event which has no outcomes

4. An event which has all only one outcome associated with it

Q.

A dice is rolled and two events P and Q are given as
P = {1, 4, 3, 5}, Q = {2, 6}

Which of the following describes the relation between P and Q?

1. Mutually exclusive events

2. Exhaustive events

3. Simple events

4. Compound events

Q.

what is compound event?

Q. Three coins are tossed once. Describe the following events associated with this random experiment:
A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(i) Which pairs of events are mutually exclusive?
(ii) Which events are elementary events?
(iii) Which events are compound events?

Q. N positive integers are multiplied together . What is the probability that last digit of the number is 5?

Q. If A and B are two events associated with a random experiment such that
P(A) = 0.5, P(B) = 0.3 and P (A ∩ B) = 0.2, find P (A ∪ B).

Q. The number of ways in which we can get a sum of $11$ by throwing three dice is :

1. $27$
2. $56$
3. $8$
4. $45$

Q.

2 dice are thrown simultaneously.Find the probability of getting

1. an even number as the sum
2. an odd number as the sum
3. the product as a perfect square

Q.

Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are

(i) mutually exclusive? (ii) simple? (iii) compound?

Q.

Which of the following is/are compound events?

1. An event where compound interest happen

2. An event which has more than one sample point

3. An event combined with another event

4. An event derived from another event

Q. Two dice are thrown. The events A, B, C, D, E and F are described as follows:
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
(i) Describe the following events:
A and B, B or C, B and C, A and E, A or F, A and F
(ii) State true or false:
(a) A and B are mutually exclusive.
(b) A and B are mutually exclusive and exhaustive events.
(c) A and C are mutually exclusive events.
(d) C and D are mutually exclusive and exhaustive events.
(e) C, D and E are mutually exclusive and exhaustive events.
(f) A' and B' are mutually exclusive events.
(g) A, B, F are mutually exclusive and exhaustive events.

Q.

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

Describe the events

(i) (ii) not B (iii) A or B

(iv) A and B (v) A but not C (vi) B or C

(vii) B and C (viii)