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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.

Let  be the number of blue marbles in the jar.  Number of green marbles in the jar =  According to question,  Number of blue marbles in the jar is 8

4. A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Total number of balls in the bag = 12 Number of black balls in the bag =  According to the question, 6 more black balls are added to the bag.  Total number of balls =  And, the new number of black balls =  Also,  The required value of is 3

3. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

Let there be  number of blue balls in the bag. Number of red balls = 5 Thus, the total number of balls = total possible outcomes =  And,  According to question, Therefore, there are 10 blue balls in the bag.  

2.(iii)   A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

Probability -A die is numbered in such a way that its faces show
What is the probability that the total score is (iii) at least 6?

+ 1 2 2 3 3 6 1 2 3 3 4 4 7 2 3 4 4 5 5 8 2 3 4 4 5 5 8 3 4 5 5 6 6 9 3 4 5 5 6 6 9 6 7 8 8 9 9 12 Total possible outcomes when two dice are thrown =  Number of times when the sum is at least 6, which means sum is greater than 5 = 15

2.(ii)   A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

Probability -A die is numbered in such a way that its faces show
What is the probability that the total score is (ii) 6 ?

+ 1 2 2 3 3 6 1 2 3 3 4 4 7 2 3 4 4 5 5 8 2 3 4 4 5 5 8 3 4 5 5 6 6 9 3 4 5 5 6 6 9 6 7 8 8 9 9 12 Total possible outcomes when two dice are thrown =  Number of times when sum is 6 = 4

1.(ii)   Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (ii) consecutive days?

Total possible ways Shyam and Ekta can visit the shop =  (2) The case that both will visit the shop on consecutive days. Shyam can go on any day between Tuesday to Friday in 4 ways. For any day that Shyam goes, Ekta will go on the next day in 1 way Similarly, Ekta can go on any day between Tuesday to Friday in 4 ways. And Shyam will go on the next day in 1 way. (Note: None of the cases repeats...
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