3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A') = 0.4. Find P(AOB) and P(AUB). Hence, state with reason whether A and B are independent events.
3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A') = 0.4. Find P(AOB) and P(AUB). Hence, state with reason whether A and B are independent events.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A')=0.4. Find
P(AOB) and P(AUB). Hence, state with reason whether A and B are independent
events.
b) A box contains 5 balls labelled 1, 2, 3, 4 and 5. A player draws a ball from the box
randomly. If the number on the ball drawn is 2, 3 or 4, the players score is that number. If
the number on the ball is 1 or 5, the player can draw a second ball without replacing the
first ball, and his score is the sum of the numbers on the two balls. The events A and B
are defined as follows
A: The score of a player is 4, 5, 6 or 7.
B: A player draws two balls from the box.
Find P(A), P(B), P(ANB) and P(AUB).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc120688-0410-477c-bb32-7a9946f2b0dc%2Ffa73c25c-57e6-420a-a17f-8ed737683aac%2F5qqv3v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3 a) The events A and B are such that P(A) =0.3, P(B'| A) =0.8 and P(B| A')=0.4. Find
P(AOB) and P(AUB). Hence, state with reason whether A and B are independent
events.
b) A box contains 5 balls labelled 1, 2, 3, 4 and 5. A player draws a ball from the box
randomly. If the number on the ball drawn is 2, 3 or 4, the players score is that number. If
the number on the ball is 1 or 5, the player can draw a second ball without replacing the
first ball, and his score is the sum of the numbers on the two balls. The events A and B
are defined as follows
A: The score of a player is 4, 5, 6 or 7.
B: A player draws two balls from the box.
Find P(A), P(B), P(ANB) and P(AUB).
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