**Q.1 A bag contains four black and five red balls, if three balls are picked at random one after another WITH replacement, what is the chance that they’re all black?**

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**A) 64/729**

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**B) 64/730**

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**C) 63/729**

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**D) 63/730**

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**Ans. A**

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**With replacement means you pick up a ball note down its color and then put it back in the bag again. So Total Number of balls remain same for each event. And Hence probability of picking a black ball (4/9) remains the same in every case.**

**1st Pick up:4/9;**

**2nd Pick up: 4/9 ;because we put the ball back in the bag, So probability is same as “1st Pick”.**

**3rd Pick up: 4/9 ;because we put the ball back in the bag.**

**So final probability**

**=1st x 2nd x 3rd**

**=4/9 x 4/9 x 4/9**

**=Cube of 4/9**

**=64/729**

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**Q.2 If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?**

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**A) Green = 3/5 ; Non-blue = 4/5**

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**B) Green = 2/5 ; Non-blue = 3/5**

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**C) Green = 4/5 ; Non-blue = 3/5**

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**D) Green = 3/5 ; Non-blue = 2/5**

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**Ans. A**

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**Total number of events = 5**

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**Q.3 A bag has 4 red balls and 2 yellow balls. (The balls are identical in all**

**respects other than colour). A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball?**

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**A) 2/3**

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**B) 2/4**

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**C) 2/5**

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**D) 2/6**

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**Ans. A**

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**There are in all (4 + 2 =) 6 outcomes of the event. Getting a red ball**

**consists of 4 outcomes.**

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**Therefore, the probability of getting a red ball is**

**4/6 = 2/3**

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**Q.4 There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football?**

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**A) 25 **

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**B) 20**

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**C) 18 **

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**D) 15**

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**Ans. B**

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**100- (50+20+10)**

**= 100-80 = 20 **

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**Q.5 In a group of persons, 70% of the persons are male and 30% of the persons are**

**married. If two-sevenths of the males are married, what fraction of the females is**

**single?**

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**A) 2/7**

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**B) 1/3**

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**C) 3/7**

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**D) 2/3**

**Ans. D**

**Let total no. of persons =100**

**Therefore total no. of males= 70**

**Total no. of females= 30**

**Given that, no. of unmarried persons =30**

**So, Number of married males=**

**2/7 * 70=20**

**Therefore, No. of married females**

**=30-20 =10**

**Therefore, No. of unmarried females**

**=30-10 = 20**

**Therefore, Required fraction of single females=**

**20/30 = 2/3**