Question

P(A) = 0.35
P(B) = 0.4
Probability of neither A nor B if
a) A and B are mutually exclusive events
b) A and B are independent events
@ganeshie8 @vishweshshrimali5 @ParthKohli

And how can a flipping of coin be dependent event?( because mutually exclusive = dependent event)

Answer 1

Mutually Exclusive: \[A\cap B = \emptyset\]
Independent: \[P(A|B)=P(A),P(B|A)=P(B)\] so... \[\frac{P(A\cap B)}{P(B)} = P(A|B)=P(A)\implies P(A\cap B) = P(A)\cdot P(?)\]

Answer 2

@Redcan I know all this. I just want to know how to solve the question

Answer 3

@nincompoop

Answer 4

@inkyvoyd

Answer 5

Properties and axioms of Probability. If E and F are two events:
\[1. P( \emptyset ) = 0\]
\[2. P(E^c)=1-P(E)\]
\[3. P(E \cup F) = P(E) + P(F) - P(E \cap F) \]
These are enough for you to find your answers.

Answer 6

hello

Answer 7

Are the answers 1 and 0.86?

Answer 8

Nope :P

Answer 9

Which is wrong?

Answer 10

@Bobo-i-bo

Answer 11

Both

Answer 12

Really? Then can you show me how to solve it?

Answer 13

@Bobo-i-bo

Answer 14

Soo... can I see your working out and attempt? That would be a good starting point ^_^

Answer 15

For a) A∩B = 0
A'UB' = (A∩B)'
A'UB' = 1-A∩B
A'UB' = 1-0
A'UB' = 1

Answer 16

@Bobo-i-bo

Answer 17

So the error is, you attempted to find
\[P(A^c \cup B^c) \]
But you should be trying to find
\[P((A \cup B)^c)\]

Answer 18

Wait a minute what is the Set notation of neither A nor B?

Answer 19

My notation:
\[A^c\]
is the same as your notation of
\[A' \]

Answer 20

I know that

Answer 21

Try drawing venn diagrams for
\[A^c \cup B^c \]
and
\[(A \cup B)^c\]

Answer 22

That will make the answer to "Wait a minute what is the Set notation of neither A nor B?" evident

Answer 23

so 0.25?

Answer 24

@Bobo-i-bo

Answer 25

yup

Answer 26

:)