The probability that a dessert sold at a certain café contains chocolate is 74%. The probability that a dessert contains both chocolate and nuts is 24%. Find the probability that a randomly chosen dessert contains nuts.

Question

bloomlocke367 · Answer

@rational

amistre64 · Answer

what happens when we add to things together, but they have parts in common?

amistre64 · Answer

|dw:1427722397011:dw|

bloomlocke367 · Answer

I'm not sure...

amistre64 · Answer

A+B = (1+2) + (2+3)
                ^^    ^^

the common parts get added a multiple of times so we have to adjust for that

in this case:

A+B = A+B-AnB

bloomlocke367 · Answer

oops... I asked the question wrong... it's what is the probability that a randomly chosen chocolate dessert contains nuts

bloomlocke367 · Answer

and what you just said confused me...

amistre64 · Answer

well i do see where i could have been clearer but im not real sure what your confusion is.

total = 1+2+3

but of we just add A and B, then we are adding a part more than once.

amistre64 · Answer

but i misread your question and thought it asked what the probability was of only nuts

amistre64 · Answer

if 74% is chocolate only, then the rest must have nuts

rational · Answer

|dw:1427722712972:dw|

amistre64 · Answer

|dw:1427722824494:dw|

amistre64 · Answer

C = y+24 = 74
N = x+24

100 = C+N-24

bloomlocke367 · Answer

I'm so confused...

anonymous · Answer

you need probability that a randomly chosen chocolate dessert contains nuts, this means you need probability that a randomly chosen contains nuts given that it contains chocolate

anonymous · Answer

A: the dessert contain nuts
B: the dessert contain chocolate

anonymous · Answer

probability that a dessert contains both chocolate and nuts  is P(A and B)
probability that a dessert  contains chocolate is P(B)

anonymous · Answer

now use the formula to get  P(A|B)

rational · Answer

since it is already known that the picked dessert is chocolate, we only look at chocolate in the venn diagram : 

1) 24% in favor of nuts 
2) total chocolates probability 74%

take the ratio for the probability that a chocolate dessert contains nuts

bloomlocke367 · Answer

ohhhh

bloomlocke367 · Answer

24/74... so 32.4%?

rational · Answer

you may also conditional probability formula for practice..

amistre64 · Answer

i see, i was stuck onthe question as it was first asked ...

bloomlocke367 · Answer

yea, sorry, my bad..

amistre64 · Answer

'sok :)

amistre64 · Answer

its hard for these old eyes to keep up with the lag freezing my screen is all

bloomlocke367 · Answer

okay.