Now suppose we repeatedly select candies with replacement. Let X be the number of
selections required to get the first cherry candy. What is P(X = 5)? Answer is 0.079. I want to know how to get this answer

Question

Now suppose we repeatedly select candies with replacement. Let X be the number of
selections required to get the first cherry candy. What is P(X = 5)? Answer is 0.079. I want to know how to get this answer

miracrown · Answer

Is this part of another problem? Something seems to be missing, we would need to know how many candies are there in total and how many of each flavor

anonymous · Answer

@Miracrown  A dish contains three cherry candies, four lemon candies and five grape candies. If we
randomly select two candies from the dish without replacement, what is the probability
that we get one cherry candy and one grape candy?
These two are together.

miracrown · Answer

3 cherry candies: O O O 
4 lemon candies: O O O O
5 grape candies: O O O O O 

How many candies are there in total?
3+4+5 = ?

anonymous · Answer

@Miracrown 12 candies. I used Binomial Distribution, but I can't get the correct answer

xapproachesinfinity · Answer

what is the prob of getting a cherry at each selection

xapproachesinfinity · Answer

since it is replacement the prob will be the same for all selection
from 1 to 5

xapproachesinfinity · Answer

now you need to figure out the prob for 1 selection

xapproachesinfinity · Answer

the prob for choosing a cherry in one selection is 3/12=1/4
yes?

xapproachesinfinity · Answer

come on you need to work here!

xapproachesinfinity · Answer

how did you do it with binomial distribution?

anonymous · Answer

@xapproachesinfinity So how to get 0.079?? I know a cherry in one selection is 0.25, but I just don't know what is next.

xapproachesinfinity · Answer

my approach appears to be wrong!
binomial distribution will work, yo most likely did
$$P(X=5)=(1/4)^5(3/4)^4$$ yes

anonymous · Answer

@xapproachesinfinity n=12, k=5 I used P(X=5) = 12C5 * $$0.25^{5}$$ $$(1-0.25)^{12-5}$$=0.1032
is not 0.079

anonymous · Answer

@xapproachesinfinity 12C5* 0.25^5 (1-0.25)^12-5

anonymous · Answer

@perl We didn't learn geometric distribution. and I know how to use it either.

perl · Answer

Let
 F = fail to pick cherry candy
S = successfully picks cherry candy
X = how many times it takes to draw a candy until you get cherry

P( X = 5) = P( pick cherry candy on fifth try)  
= P ( FFFFS) 
= P( F) * P(F) * P(F) * P(F) * P(S) 
= 9/12 * 9/12 * 9/12 * 9/12 * 3/12  
=.0791

anonymous · Answer

@perl thanks a lot!!