Question 6

2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Answer

Let us denote 2 boys and 2 girls in room X as B1, B2 and G1, G2 respectively. Let us denote 1 boy and 3 girls in room Y as B3, and G3, G4, G5 respectively.

Accordingly, the required sample space is given by S = {XB1, XB2, XG1, XG2, YB3, YG3, YG4, YG5}

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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

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- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

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How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

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(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

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Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

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How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

- Q:-
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …

- Q:-
A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.

- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:-
Find the sum to

*n*terms in the geometric progression - 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:-
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?

- Q:-
Find the sum to

*n*terms of the series 1^{2}+ (1^{2}+ 2^{2}) + (1^{2}+ 2^{2}+ 3^{2}) + …

- NCERT Chapter