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Question
A primary school teacher wants to teach the concept of 'larger number' to the students of Class II.
To teach this concept, he conducts an activity in his class. He asks the children to select two numbers from a set of numbers given as 2, 3, 4, 5 one after the other without replacement.
All the outcomes of this activity are tabulated in the form of ordered pairs given below:
| 2 | 3 | 4 | 5 | |
| 2 | (2, 2) | (2, 3) | (2, 4) | |
| 3 | (3, 2) | (3, 3) | (3, 5) | |
| 4 | (4, 2) | (4, 4) | (4, 5) | |
| 5 | (5, 3) | (5, 4) | (5, 5) |
- Complete the table given above.
- Find the total number of ordered pairs having one larger number.
- Let the random variable X denote the larger of two numbers in the ordered pair.
Now, complete the probability distribution table for X given below.
X 3 4 5 P(X = x) - Find the value of P(X < 5)
- Calculate the expected value of the probability distribution.
Solution
i.
| 2 | 3 | 4 | 5 | |
| 2 | (2, 2) | (2, 3) | (2, 4) | (2, 5) |
| 3 | (3, 2) | (3, 3) | (3, 4) | (3, 5) |
| 4 | (4, 2) | (4, 3) | (4, 4) | (4, 5) |
| 5 | (5, 2) | (5, 3) | (5, 4) | (5, 5) |
ii. Total number of ordered pairings with one greater number = 12
iii.
| X | 3 | 4 | 5 |
| P(X = x) | `2/12` | `4/12` | `6/12` |
iv. P(X < 5) = P(3) + P(4)
`2/12 + 4/12 = 6/12`
P(X < 5) = `1/2`
v. E(x) = ∑xP(x)
= `3 xx 2/12 + 4 xx 4/12 + 5 xx 6/12`
= `6/12 + 16/12 + 30/12`
= `52/12`
= `13/3`
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