16

Q1. Two students Amit and Priyanka appeared in an examination. The probability that Amit will qualify the examination is 0.06 and that Priyanka will qualify the examination is 0.12. The probability that both will qualify the examination is 0.02. Then, the probability that both Amit and Priyanka will not qualify the examination is:

• 0.84
• 0.45
• 0.12
• 0.91

Solution

Let A and B denote the events that Amit and Priyanka will qualify the examination, respectively. Given that P (A) = 0.06, P (B) = 0.12 and P (A  B) = 0.02 Then, the event  that both Amit and Priyanka will not qualify the examination may be expressed as Since, i.e., Amit will not qualify the examination and  i.e., Priyanka will not qualify the examination. Also  =                                (By Demorgan"s Law) Now P (A B) = P (A) + P (B) - P (A  B) Or P (A B) = 0.06 + 0.12 - 0.02 = 0.16 Therefore P () =  = 1 - P (A  B) = 1 - 0.16 = 0.84

Q2. A bag contains 12 red balls, 10 white balls and 8 green balls. One ball is drawn from the bag, then the probability that the drawn ball is neither red nor green is:

• 1/3
• 1/2
• 1/4

Solution

Number of red balls = 12 Number of white balls = 10 Number of green balls = 8 Therefore, total number of balls in bag = 30 Favorable elementary event for drawn neither red nor green ball = 30 – 12 – 8 = 10 So, required probability = 

Q3.  The probability that a leap year selected at random will have 53 Sundays is

• 1/7
• 2/7
• 3/7
• 4/7

Solution

A leap year has 366 days52 weeks and 2 days. 52 weeks will have 52 Sundays the remaining two days can be (S,M),(M,T),(T,W),(W,T),(T,F),(F,S),(S,S) Out of the 7 possibilities 2 are favourable i.e. (S,M),(S,S) So the required probability is 2/7.

Q4. One card is drawn from a well shuffled pack of 52 cards. If each outcome is equally likely, what is the probability that the card will be a red card?

• 1/4
• 1/3
• 1/2
• 2/3

Solution

There are total 52 cards, of which 26 are red, So probability of drawing a card that is red  is 26/52=1/2.

Q5. When two dice are thrown what’s the probability of getting a sum less than 4?

• 1/6
• 5/6
• 1/12
• 5/12

Solution

The sample space for the event of getting a total <4 is ={(1,1),(1,2),(2,1)} The total number of possibilities is 36. Hence the required probability =3/36=1/12

Q6. The set of all possible outcomes of a random experiment is called the …… associated with the experiment.

• Experiment
• Event
• Sample space
• Outcomes

Solution

The&nbnbsp;set of all possible outcomes of a random experiment is called the sample space associated with the experiment.

Q7. The sample space associated to thrown a dice is:

• (1, 2, 3)
• (2, 4, 6)
• (1, 3, 5)
• (1, 2, 3, 4, 5, 6)

Solution

The sample space associated to thrown a dice is (1, 2, 3, 4, 5, 6).

Q8. A four digit number is formed by using the digits 1,2,3,4,5,6,7 without repetition. What is the probability that it's divisible by 2?

• 1/7
• 2/7
• 3/7
• 4/7

Solution

A four digit number out of the  given digits can be formed by filling the first place by any of the 7 digits, second by any of the remaining 6 digits, third by any of the remaining 5 digits and last place by any of the remaining the 4 digits.i.e. in ⁷P₄  ways=840 ways. To form an even number the unit's   place can be filled up by any one of the digits 2, 4 or 6.i.e. in 3 ways. For the other places, we have respectively remaining 6, 5 and 4 digits left. So this job can be done in ⁶P₃ ways. So total number of ways =3 x (⁶P₃) =360. So, the required probability=360/840=3/7.

Q9. A coin is tossed twice. What is the probability that atleast one tail occurs?

• 1/2
• 1/4
• 3/4
• 1

Solution

When a coin is tossed twice, it’s the same as tossing two coins together. So the outcomes are HH, HT, TH, TT. Thus, getting at least one tail is an event which has the probability ¾.

Q10. The sample space of an experiment is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} and A = {TTT}, B = {HTT, THT, TTH}, C = {HHT, HTH, THH, HHH}, then A, B and C form a set of?

• Mutually exclusive but not exhaustive events
• Exhaustive but not mutually exclusive events
• Mutually exclusive and exhaustive events
• Neither mutually exclusive nor exhaustive events

Solution

Q11. Two dice are thrown simultaneously. The probability of getting an even number as the sum is:

• 1/2
• 1/4
• 1/3
• 1

Solution

When two dice are thrown, then number of elements in sample space = 36 Let the event A is the event for an even number as the sum on both dice. Then, A = Therefore, number of elements in event A = 18

Q12. The events when we have no reason to believe that one is more likely to occur than the other is called:

• Dependent event
• Independent events
• Equally likely events
• Not equally likely events

Solution

The events when we have no reason to believe that one is more likely to occur than the other are called equally likely events.

Q13. An experiment involves rolling a pair of dice and recording the number that comes up. Suppose, A: the sum is greater than 8. B: 2 occurs on either die. Then A and B are ....... events.

• Mutually exclusive events
• Exhaustive events
• Favorable events
• Random experiment

Solution

The sample space associated with the given experiment is given by We have, A = the sum is greater than 8 B = 2 occurs on either die Since, A B =  So, A and B are mutually exclusive events.

Q14. A box contains 5 defective and 15 non defective bulbs. Two balls are chosen at random, find the probability that both the bulbs are non defective?

• 5/19
• 10/38
• 21/38
• Non of the above

Solution

Two bulbs can be chosen from 20 bulbs in  ways. 2 non defective bulbs can be chosen from 15 non defective bulbs in  ways. the required probability is 

Q15. In a simultaneous toss of two coins, the probability of getting no tail is:

• 1/2
• 1/4
• 2
• 0.1

Solution

The sample space associated to the given random experiment is given by S = (HH, HT, TH, TT), there are 4 elements in S, Therefore, total number of elementary events = 4 Event for getting no tail is only one (HH) So, required probability = .

Q16. If an event has more than one sample point, it is called a ………

• Compound event
• Simple event
• Exhaustive event
• Mutually exclusive event

Solution

If an event has more than one sample point, it is called a compound event.

Q17. Tickets are numbered from 1 to 18 are mixed up together and then a ticket is drawn at random. Find the probability that the ticket has a number which is a multiple of 2 or 3?

• 1/3
• 3/5
• 2/3
• 5/6

Solution

Sample space S={1,2,....18} Let A be the set of multiple of 2={2,4,6,8,10,12,14,16,18} B be the set of multiple of 3={3,6,9,12,15,18}

Q18. One card is drawn from a well shuffled pack of 52 cards. If each outcome is equally likely, what is the probability that the card will not be a red card?

• 1/4
• 1/3
• 1/2
• 2/3

Solution

There are total 52 cards, of which 26 are red, this means remaining 26 are non black. So probability of drawing a card that is not  red  is 26/52=1/2.

Q19. The probability on the basis of observations and collected data is called:

• Statistical approach of probability
• Classical approach of probability
• Axiomatic approach of probability
• Empirical probability

Solution

The probability on the basis of observations and collected data is called statistical approach of probability.

Q20. Three fair coins are tossed simultaneously what is the probability of getting more heads than the number of tails?

• 2/5
• 7/8
• 5/8
• 1/2

Take Another Test