| Q1. |
If P(A) = 3/5 and P(B)=1/5, find P (AB) if A and B are independent events. |
| Q2. |
Let f: NY be a function defined as f(x) = 4x + 3, where, Y={ye N: y=4x + 3 for some x ∈ N). Show that fis invertible. Find the inverse. |
| Q3. |
A fair coin and an unbiased die are tossed. Let A be the event 'head appears on the coin' and B be the event '3 on the die'. Check whether A and B are independent events or not. |
| Q4. |
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event 'the number is even,' and B be the event 'the number is red. ' Are A and B independent? |
| Q5. |
Let E and F be events with P(E) = P(F) =1 and P (EF) = 3. Are 10 E and F independent? |
| Q6. |
Given that the events A and B are such that P(A) = P(AUB) = 3/5 and P(B)=p. Find p if they are (i) mutually exclusive and (ii) independent. |
| Q7. |
Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find
(i) P(A∩B) (ii) P(AUB) (iii) P(AIB) (iv) P(BIA) |
| Q8. |
If A and B are two events such that P(A) = 1/4 P/B = 1/2 and P (A~ B) = 1/8, find P (not A and not B) |
| Q9. |
Let A (1.2.3. B- (4, 5, 6, 7) and let f= {(1, 4), (2, 5), (3.6)) be a from A to B. Show that fis one-one. |
| Q10. |
In each of the following cases, state whether the function is one-one, onto, or objective. Justify your answer. (1) f: R R defined by f(x) = 3-4x
|
| Q11. |
Let AR- (3) and B = R - {1}. Consider the function f:
A→ B detined by (x)=(二) x-2 x-3 Is f one-one and onto? Justify your answer. |
| Q12. |
Show that the function f: R, R, defined by f(x) = 1 X is one-one and onto, where R, is the set of all non-zero real numbers. Is the result true if thermomain R is replaced by N with the co-domain being the same as R? |
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