Ricky has a dumpling five-shooter with one dumpling in one of the five chambers. He spins it and fires, repeating this two-step process until he gets the dumpling to come out. What is the probability that he gets the dumpling to come out on the 2nd or 4th shot? Answer should be a common fraction

i know the denominator is 625, but am confused on how to get the numerator

xxJenny1213xx Mar 19, 2021

#1**0 **

Did the question include the probability of the dumpling coming out?

Or perhaps I'm missing something.

=^._.^=

catmg Mar 19, 2021

#5**0 **

I probably won't help but it might.

The probability of the dumpling being shot out on the first try is 1/5. The probability of it being shot out on the second try is 1/4 because there are only 4 places where the dumpling can be shot out of. The third is 1/3. The fourth is 1/2. The fifth is 1 because it is the only place where the dumpling can be shot out of.

Guest Mar 19, 2021

#6**0 **

i see where you are going but how do i calculate it getting shot out from the 2nd or 4th time?

xxJenny1213xx
Mar 19, 2021

#7**0 **

You most likely have to calculate the total probability (the denominator). Idk if this next step is right. You have to add the 2nd shot probability to the 4th shot probability. 1/4+1/2=3/8? Then find the numerator by multiplying the denominator by 3/8?

Btw, you are not multiplying the 2nd and the 4th because we are not trying to find if both have the dumpling shot out. So add.

MobiusLoops
Mar 19, 2021

#10**+2 **

Ricky has a dumpling five-shooter with one dumpling in one of the five chambers. He spins it and fires, repeating this two-step process until he gets the dumpling to come out. What is the probability that he gets the dumpling to come out on the 2nd or 4th shot? Answer should be a common fraction

i know the denominator is 625, but am confused on how to get the numerator

\(P(1st\; shot)=\frac{1}{5}\\ P(2nd\; shot)=\frac{4}{5}*\frac{1}{5}\qquad\qquad=\frac{4}{25}\quad=\frac{100}{625}\\ P(3rd\; shot)=\frac{4}{5}*\frac{4}{5}*\frac{1}{5}\\ P(4th\; shot)=\frac{4}{5}*\frac{4}{5}*\frac{4}{5}*\frac{1}{5}\qquad\qquad=\frac{64}{625}\\ P(5th\; shot)=\frac{4}{5}*\frac{4}{5}*\frac{4}{5}*\frac{4}{5}*\frac{1}{5}\\~\\ P(2nd\;or\; 4th)=\frac{164}{625} \)

Melody Mar 20, 2021