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Question 5

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3.

Find the number of blue balls in the jar.

Answer

Total no of marbles in the jar (green + blue) = 24

Let the no of green marbles be = x

Therefore, no of blue marbles left = 24 – x

P(E) of marble to be green = 2/3 {Given} …....(I)

Acc. to question

P(E) of green marble = x/24 …..........(ii)

Equating equation (I) and (ii)

2/3 = x/24

x = 16

No of green marbles = 16

Hence, no of blue marbles = 24- 16 = 8

- Q:-
Refer to Example 13. (i) Complete the following table:

(ii) A student argues that ‘there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability

Do you agree with this argument? Justify your answer.

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- Q:-
Which of the following experiments have equally likely outcomes? Explain.

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(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

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- Q:-
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(i) Probability of an event E + Probability of the event ‘not E’ =

(ii) The probability of an event that cannot happen is

(iii) The probability of an event that is certain to happen is

(iv) The sum of the probabilities of all the elementary events of an experiment is(v) The probability of an event is greater than or equal to

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- Q:-
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Represent the following situations in the form of quadratic equations :

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(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

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An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

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Solve the following pair of linear equations by the substitution method.

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Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

- Q:-
Form the pair of linear equations for the following problems and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them.

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

(v) A fraction becomes, , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes Find the fraction.(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

- Q:-
Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

- Q:-
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