Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): A random variable X has the following probability distribution
|
X |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
P(X) |
0.2 |
0.1 |
0.05 |
0.15 |
0.1 |
0.07 |
0.12 |
0.13 |
0.08 |
If events E = {X is greater than 5}, F = {X is an odd number}, then $P(E∪F) = 0.65$.
Reason (R): $E∪F = \{1, 3, 5, 6, 7, 8, 9\}$.
Select the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Assertion (A) is false, but Reason (R) is true.
E = {X is greater than 5}
$⇒ E = \{6, 7, 8, 9\}$
F = {X is an odd number}
$⇒ F = \{1,3,5,7,9\}$.
So, $E∪F = \{1,3,5, 6, 7, 8, 9\}$
∴ Reason is true.
Now, $P(E∪F) = P(1) + P(3) + P(5) + P(6) + P(7) + P(8) + P(9)$
$= 0.2+0.05+0.1+0.07 +0.12 + 0.13 +0.08$
$= 0.75$
∴ Assertion is false.