Probability

[west garnet]

<@&791435371564892232>

[west garnet]

@limber crest

[gentle fog]

if they are mutually exclusive they cannnot occur at the same time so P(A ∩ B) = 0

if that's true then P(A ∪ B) = P(A) + P(B)

[west garnet]

yeah

so how do you find p

[gentle fog]

0.64 = 2p

[west garnet]

how

[gentle fog]

P(A ∪ B) = 0.64
P(A) = p
P(B) = p

[west garnet]

okay

so p = 0.32

[gentle fog]

and P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

[gentle fog]

yes

[west garnet]

so p(a) = 0.16

[gentle fog]

no

0.32

[west garnet]

both?

[gentle fog]

P(A) = P(B) = 0.32

[west garnet]

Okay

so if i do

p (aub) = 0.32 + 0.32 - (0.32)^2

[gentle fog]

that is not how you do part b

[west garnet]

okay

but p(aub) = p(a) + p(b) - (AnB)

[gentle fog]

but it says given that ....

[west garnet]

ahhh

[gentle fog]

and the fact they are independent means that P(A ∩ B) = P(A) * P(B)

for part b

[west garnet]

yeah

0.32 squared

okay then

0.1024

[gentle fog]

don't use this for part b

it says "given instead that..."

so part a doesn't matter

[west garnet]

oh

So fresh start idk anything

[gentle fog]

yes

apart from P(A ∩ B) = P(A) * P(B)

since the events are independent

[west garnet]

So Couldnt i just use quadratic formula

[gentle fog]

if you find the value of k then yeh

[west garnet]

hang on what

my teacher cant teach so

im still learning

and im like huh

explain part b as if im 5

[gentle fog]

so since the events are independent P(A ∩ B) = P(A) * P(B)
we know that P(A ∪ B) = 0.64
and that P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
so 0.64 = 2p - p^2

p^2 - 2p + 0.64 = 0

but we need to multiply by 25 to get the form they want

[west garnet]

that actually makes sense

thank you

[gentle fog]

👍

[west garnet]

could you help me in