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53. If 4-digit numbers greater than 5,000 are randomly formed from the digits0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) The digits are repeated? (ii) The repetition of digits is not allowed?
53. If 4-digit numbers greater than 5,000 are randomly formed from the digits0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) The digits are repeated? (ii) The repetition of digits is not allowed?
53. (a) No. of ways of forming a four-digit number greater than 5000 from the given digit 0, 1, 3, 5, 7. and digit repetition is allowed can be done in such a way either 5 or 7 and occupy the thousands' place and any of the digits 0, 1, 3, 5, 7 can occupy the remaining 3 places.
Hence,
Upvote 
52. From the employees of a company, 5 persons are selected to represent them inthe managing committee of the company. Particulars of five persons are as follows:
1. No. Name Sex Age in years
2. Harish M 30
3. Rohan M 33
4. Sheetal F 46
5. Alis F 28
6. Salim M 41
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
52. From the employees of a company, 5 persons are selected to represent them inthe managing committee of the company. Particulars of five persons are as follows:
1. No. Name Sex Age in years
2. Harish M 30
3. Rohan M 33
4. Sheetal F 46
5. Alis F 28
6. Salim M 41
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
52. Total no. of person selected to represent the company n (s) = 5.
Let A: person is male.
A = {Harish, Rohan, Salim}
n (A) = 3
And B: person has one 35 yes of age.
B = {Sheetal, Salim}
n (B) = 2
And A ∩ B = {Salim}
n (A ∩ B) = 1
Probability that person is either male or over 35 years.
= P (A ∪ B) = P (A) +
Upvote 51. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35.
Find (i) P(A ∪ B) (ii) P(A´ ∩ B´) (iii) P(A ∩ B´) (iv) P(B ∩ A´)
51. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35.
Find (i) P(A ∪ B) (ii) P(A´ ∩ B´) (iii) P(A ∩ B´) (iv) P(B ∩ A´)
51. Given, P (A) = 0.54
P (B) = 0.69.
P (A ∩ B) = 0.35.
(i) P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
= 0.54 + 0.69 - 0.35
= 0. 88
(ii) P (A? ∩ B? ) = P (A ∩ B)? = 1 - P (A ∪ B) = 1 - 0.88 = 0.12
(iii) P (A ∩ B? ) = P (A) - P (A ∩ B)
= 0.54 - 0. 35 = 0.19
(iv) P (B ∩ A? ) = P (B) - P (A ∩ B) = 0.69 - 0.35 =
Upvote 50. Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
50. Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
49. Out of 100 students, two sections of 40 and 60 are formed. If you and your friendare among the 100 students, what is the probability that
(a) You both enter the same section?
(b) You both enter the different sections?
49. Out of 100 students, two sections of 40 and 60 are formed. If you and your friendare among the 100 students, what is the probability that
(a) You both enter the same section?
(b) You both enter the different sections?
49. Here, out of 100 students, first section has 40 students and the rest I e, 60 students enters in second section.
As me and my friend are among the 100 students.
The no. of ways of selecting 2 students from the 100 students
= 100C2
(a) When both enters first section if 2 of us are among the 40 stud
Upvote 48. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) One ticket (b) Two tickets (c) 10 tickets.
48. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) One ticket (b) Two tickets (c) 10 tickets.
48. Total no. of ticket for lottery sold = 10, 000
No. of ticket that are awarded prize = 10
So, no. of ticket that are not awarded prize = 10.000 - 10
= 9990
(a) Now, probability of met getting a prize if we buy one ticket
Upvote 47. A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)
47. A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)
47. Since the die has two faces each mark 1, three faces each marks 2 and one face mark 3.
The possible sample space of outcome is.
S = {1, 2, 3} so, n (s) = 6
(i) P (2)
(ii) P (1 or 3) = P (1) + P (3) =
(iii) P (not 3) = 1 P (3) = 1 - =
Upvote 46. 4 cards are drawn from a well – shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
46. 4 cards are drawn from a well – shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
46. Total number of ways of drawing 4 cards from a duck of 52 cards, n (s) = 52C4
Total no. of diamond cards = 13
Similarly, total. no. of spades cards = 13
Upvote 45. A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that
(i) All will be blue? (ii) Atleast one will be green?
45. A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that
(i) All will be blue? (ii) Atleast one will be green?
45. Given,
No. of red marbles= 10
No. of blue marbles = 20
No. of green marbles = 30.
So, total no. of marbles = 10 + 20 + 30 = 60
Now, we are to select 5 marbles from the given 60 marbles.
So the sample space is:
n (s) = 60c5.
Upvote 44. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted fo rboth NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student has opted NSS but not NCC.
44. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted fo rboth NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student has opted NSS but not NCC.
44. Given that, total number of student, n (S) = 60
Let A: student opted for NCC
n (A) = 30
B: student opted for NSS
n (B) = 32
And student who opted both NCC and NSS, n (A∩B) = 24
(i) Probability that student opted for NCC or NSS,
P (A∪B) = P (A) + P (B) – P (A∩B)
(ii) Probability that student opted nei
Upvote