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Check whether the following probabilities P(A) and P(B) are consistently defined
P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Concept: undefined >> undefined
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| `1/3` | `1/5` | `1/15` | .... |
Concept: undefined >> undefined
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Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.35 | ... | 0.25 | 0.6 |
Concept: undefined >> undefined
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.5 | 0.35 | .... | 0.7 |
Concept: undefined >> undefined
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 all will be blue?
Concept: undefined >> undefined
4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Concept: undefined >> undefined
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:
| S. No. | Name | Sex | Age in years |
| 1. | Harish | M | 30 |
| 2. | Rohan | M | 33 |
| 3. | Sheetal | F | 46 |
| 4. | Alis | F | 28 |
| 5. | 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?
Concept: undefined >> undefined
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, the digits are repeated?
Concept: undefined >> undefined
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
Concept: undefined >> undefined
Find the mean and standard deviation using short-cut method.
| xi | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 |
| fi | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |
Concept: undefined >> undefined
Find the mean, variance and standard deviation using short-cut method.
| Height in cms | 70 - 75 | 75 - 80 | 80 - 85 | 85 - 90 | 90 - 95 | 95 - 100 | 100 - 105 | 105 - 110 | 110 - 115 |
| No. of children | 3 | 4 | 7 | 7 | 15 | 9 | 6 | 6 | 3 |
Concept: undefined >> undefined
From the prices of shares X and Y below, find out which is more stable in value:
|
X |
35 |
54 |
52 |
53 |
56 |
58 |
52 |
50 |
51 |
49 |
|
Y |
108 |
107 |
105 |
105 |
106 |
107 |
104 |
103 |
104 |
101 |
Concept: undefined >> undefined
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results::
|
Firm A |
Firm B |
|
|
No. of wage earners |
586 |
648 |
|
Mean of monthly wages |
Rs 5253 |
Rs 5253 |
|
Variance of the distribution of wages |
100 |
121 |
(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm, A or B, shows greater variability in individual wages?
Concept: undefined >> undefined
If A and B are two set such that \[A \subset B\]then find:
\[A \cap B\]
Concept: undefined >> undefined
If A and B are two sets such that \[A \subset B\] then find:
\[A \cup B\]
Concept: undefined >> undefined
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[A \cup B\]
Concept: undefined >> undefined
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[A \cup C\]
Concept: undefined >> undefined
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[B \cup C\]
Concept: undefined >> undefined
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find\[B \cup D\]
Concept: undefined >> undefined
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[A \cup B \cup C\]
Concept: undefined >> undefined
