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Theoretical Probability vs Experimental Probability

Sort the even...

Question

Sort the events in increasing order of the no. of sample points (Event with least number of sample points at the top).

A

Tossing 2 coins

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B

Rolling of a die

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C

Tossing 3 coins

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D

Rolling 2 dices

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Solution

The outcomes on tossing two coins are: (HH, TT, TH , HT).
So, the total number of outcomes = 4.

The outcomes on rolling a die is: (1, 2, 3 , 4, 5, 6)
So, the total number of outcomes = 6.

The outcomes on tossing three coins are: (HHH, TTT, THH , THT, TTH, HTH, HHT, HTT).
So, the total number of outcomes = 8.

The outcomes on rolling two dices are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2,2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3,2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4,2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5,2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6,2), (6, 3), (6, 4), (6, 5), (6, 6)
So, the total number of outcomes = 36.

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Similar questions

Q. In each of the following experiments write the sample space S, number of sample points n(S), events P, Q, R using set form and n(P), n(Q) and n(R).
Find the events among the events defined above which are:
complementary events, mutually exclusive events and exhaustive events

(i) Three coins are tossed simultaneously:
P is the event of getting at least two heads.
Q is the event of getting no head.
Q is the event of getting head on second coin.

Q. In each of the following experiments, write the sample space S, numberr of sample points n(S), event A,B,C and n(A), n(B), n(C), also find complementary events, mutually exclusive events:

(i) Two coins are tossed, A is the event of getting at most one head, B is the event getting both heads, C is the event of getting same face on both the coins.

Q. In each of the following experiments, write the sample space S, number of sample points n(S), event A,B,C and n(A), n(B), n(C), also find complementary events, mutually exclusive events:

Two dice are thrown, A is the event that the sum of the numbers on their upper face is at least nine, B is the event that the sum of the numbers on their upper face is divisible by 8, C is the event that the same number on the upper faces of both dice.

Q. In each of the following experiments, write the sample space S, number of sample points n(S), event A,B,C and n(A), n(B), n(C), also find complementary events, mutually exclusive events:

A coin is tossed three times.A is the event that head appears once, B is the event that head appeared at the most twice, C is the event that tail does not appear.

Q. Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).
(1) One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.

(2) Two dice are rolled simultaneously,
Event A : The sum of the digits on upper faces is a multiple of 6.
Event B : The sum of the digits on the upper faces is minimum 10.
Event C : The same digit on both the upper faces.

(3) Three coins are tossed simultaneously.
Condition for event A : To get at least two heads.
Condition for event B : To get no head.
Condition for event C : To get head on the second coin.

(4) Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.
Condition for event A : The number formed is even
Condition for event B : The number formed is divisible by 3.
Condition for event C : The number formed is greater than 50.

(5) From three men and two women, environment committee of two persons is to be formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed.
Condition for event C : There should not be a woman member.

(6) One coin and one die are thrown simultaneously.
Condition for event A : To get head and an odd number.
Condition for event B : To get a head or tail and an even number.
Condition for event C : Number on the upper face is greater than 7 and tail on the coin.

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