05-09-2021 Answers

 1. In a class 52% of the students are girls of which 25% are interested in tennis. What is the probability that a randomly selected student from the class is a girl who is interested in tennis?

Answer: 13/100

Solution: Assume 100 students are in the class.

Num of girls = 52

Girls interested in tennis = 52 * 25/100 = 13

Reqd probability = 13/100

2. On a highway, the probability of seeing an ambulance during a twenty-minutes period is 11/36. What is the probability of not seeing an ambulance in a ten-minutes period?

Answer: 5/6

Solution: Probability of not seeing an ambulance in 20 mins period = 1 - 11/36 = 25/36

Probability of not seeing a lorry in 10 mins period = Square root of 25/36 = 5/6

3. Find the probability that 2 men selected at random were born in the same month.

Answer: 1/12

Solution: The first person can be born in any of the 12 months.

The second person also being born in the same month = 1/12.

4. Four boys and three girls stand in queue for an interview. The probability that they stand in alternate positions is

Answer: 1/35

Solution: Total ways of arrangement = 7!

Ways to arrange them in alternate positions like B G B G B G B is = 4! * 3!

Total probability = 4! * 3!/7! = (3*2)/(5*6*7) = 1/35

5. A bag has 40 different colours of balls, 25 red, 10 white and 5 black. If a ball is chosen at random, what is the probability of that it is not red?

Answer: 3/8

Solution: The probability that the selection is a red ball = 25/40 = 5/8.

So the required probability is 1 - 5/8 = 3/8.

6. In a lottery draw, there are 20 prizes and 40 blanks. A lottery is drawn at random. What is the probability of not getting a prize?

Answer: 2/3

Solution: There are total 20+40 = 60 lotteries.

The required probability of not getting a prize = 40/60 = 2/3.

7. From a standard pack of cards, Reena picks up a card and replaces it until she picks a king or a spade. What is the probability that the final card picked up is a king?

Answer: 1/4

Solution: The final card can be either a spade (13 cards) including a spade king or the remaining three kings (king of diamond, club and heart).

Hence the sample space contains 13+3 = 16 cards.

Out of these 16 cards, 4 are kings.

Hence required probability = 4/16 = 1/4

8. A number lock contains two rolls with each roll having the digits 0 to 9. Find the probability that the lock can be opened successfully in first attempt.

Answer: 1/100

Solution: Probability of choosing the correct number in first roll = 1/10 (10 numbers are there from 0 to 9), second roll = 1/10.

Hence required probability = 1/10 * 1/10 = 1/100.

9. If two dice are rolled three times, what is the probability that the two dice will display the same number during one of the three rolls?

Answer: 91/216

Solution: There are 6 distinct numbers in 6 faces of the dice.

In one roll, the probability of dice not matching is 5/6. (Based on conditional probability the second not displaying the number on first = 5/6).

Hence the probability of not matching in three rolls (as each roll is independent) = 5/6 * 5/6 * 5/6 = 125/216.

Hence probability of matching (display the same number) during one of the three rolls = 1 - 125/216 = 91/216

10. The Beach line train starts at 5.00 AM from Central station and the Fort line train starts at 5.02 AM from Central. Each line has trains starting at an interval of every 10 minutes. The duration of the service is from 5.00 AM to 11.00 PM. Babu goes to his office either using Beach line or Fort line. If he reaches Central station at a random time between 7.00 AM and 4.00PM and what is the probability of Babu boarding Beach line train to go to his office?

Answer: 0.8

Solution: In a 10mins interval, 8 mins duration is for Beach line and 2 mins for Fort line.

Hence probability of boaring Beach line = 8/10 = 0.8

11. What is the probability of getting sum 2 in a throw of dice?

Answer: 1/36

Solution: 2 can occur only when (1,1) occurs.

Total sample space = 36.

Hence probability = 1/36

12. Among the families with two children, which have at least one girl, what is the probability that the family has two girls?

Answer: 1/3

Solution: It is given the families are with two children having atleast one girl.

So the possible three combinations are Boy-Girl, Girl-Boy, Girl-Girl.

Among these only one has two girls.

Hence required probability = 1/3

13. There are 2 positive integers A and B. What is the probability that A+B is odd?

Answer: 1/2

Solution: When A and B are odd, A+B is even

When A and B are even, A+B is even

When A is odd and B is even A+B is  odd.

When A is even and B is odd A+B is odd.

Hence reqd probability = 2/4 = 1/2

14. Anil and Babu throw a die each. What is Babu's chance (probability) of throwing a lesser number when A throws 5?

Answer: 1/9

Solution: Probability of Anil throwing 5 = 1/6 

Numbers that can appear on die = 1 to 6 = 6

Numbers that should appear for Babu to throw a lesser number (than 5) = 1 to 4 = 4.

Required Probability = 1/6 * 4/6 = 1/9

15. A typist prepared 3 different letters to be sent to 3 different addresses. For each letter, she prepared an envelope with its correct address. If the 3 letters are to be put into the 3 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?

Answer: 1/2

Solution: Let the letters be A,B,C

Probability that A is in the right envelope= 1/3

Probability that B is in wrong envelope = 1/2

Probability that C is in wrong envelope = 1

Hence probability that only A is in right envelope = 1/3 * 1/2 * 1 = 1/6.

Hence considering A, B and C, required probability = Num of letters * 1/6 = 3 * 1/6 = 1/2

16. One card is lost out of 52 cards. Two cards are drawn randomly. They are spade. What is the probability that the lost card is also spade?

Answer: 11/50

Solution: It is given the drawn cards are spades. So probability that the lost card was also spade = (13-2)/(52-2) = 11/50

17. A fruit basket has 6 apples and 4 mangoes. If two fruits are picked randomly, what is the probability that both fruits are apple?

Answer: 1/3

Solution: Probability of first fruit being apple = 6/(6+4) = 6/10.

After picking first fruit now 9 remain out of which 5 are apples.

Hence probability of second fruit being apple = 5/9.

Required probability = 6/10 *  5/9  = 30/90 = 1/3

18. A problem is given to three students, Ajay, Bijay and Chandan independently. If their chances of solving the problem are 60%, 50% and 40%, what is the probability the problem will be solved?

Answer: 22/25

Solution: Probability (problem is solved) = 1 – Probability (problem is not solved)

= 1 – Probability(none solves the problem)

= 1 – [4/10 * 5/10 * 6/10]

= 22/25.

19. Madan has nine cards from number 2 to 9 of diamond in a shuffled manner. What is the probability of drawing two cards in sequence from the hand such that each card selected contains a smaller number than the previous one?

Answer: 1/2

Solution: The number of possible permutations of the numbers on the two cards drawn = 2P2 = 1

Out of these two ways of arrangement of distinct numbers, only one is in decreasing ordeer.

Hence the required probability = 1/2.

In problems similar to this it does not matter how many cards were present initially.

20. The probability that an arrow fired will hit the target is 1/4. Three arrows are fired towards the target. What is the probability that the target will be hit?

Answer: 37/64

Solution: The probability that the target will not be hit = 3/4 * 3/4 * 3/4 = 27/64

Hence reqd prob = 1 - 27/64 = 37/64