Probability Question !! 10 point for the right answer?

Question

"you are eating a bowl of nuts. 40% of the nuts are almonds and the rest are peanuts, 45% of the almonds are salted. 65% of the peanuts are salted. you reach in and grab a nut. the probability that it is a rotten salted almond is 5%. the prob. that it is an unsalted almond that is not rotten is 8%. the probability that it is rotten given that it is a peanut is 45%. you eat a nut and notice it is not Rotten. what is the probability that it is a peanut?

Answer 1

The breakdown is as follows

Almonds: 40% / salted 45% < rotten = 0.40 x 0.45 x n = 5%
........................ \ unsalted 55% < not rotten = 0.40 x 0.55 x p = 8%

Peanuts: 60% / salted 65%
....................... \ unsalted 35%

n = 0.05 / (0.40 x 0.45) = 27.78%
1-n = 72.22%

p = 0.08 / (0.40 x 0.55) = 36.36%
1-p = 63.636%

So, the diagram expands as follows:
Almonds: 40% / salted 45% / rotten = 27.78%
........................ \ ...................\ not rotten = 72.22%
.......................... \ unsalted 55% / rotten = 63.636%
........................... ........................\ not rotten = 36.36%

Peanuts: 60% / salted 65% / rotten
....................... \ ...................\ not rotten
........................ \ unsalted 35% / rotten
......................... ....................... \ not rotten

The probability it is not rotten, given it is an almond is:
almond salted not rotten = 45% * 72.22% = 32.5%
almond unsalted not rotten = 55% * 36.36% = 20%
32.5% + 20% = 52.5%

The probability it is not rotten, given it is a peanut is (1 - 0.45) = 55%.

The final break down is:
Non-rotten almond = 0.40 x 0.525 = 0.21
Non-rotten peanut = 0.60 x 0.55 = 0.33

That brings us to just the non-rotten nuts.
Almond, given non-rotten = 0.21 / 0.54 = 38.889%
Peanut, given non-rotten = 0.33 / 0.54 = 61.111%

Given that a chosen nut is not rotten, the probability it is a peanut is 61.111%

Answer 2

60%.

40% of the nuts are almonds and the rest are peanuts. That means grab any nut and it's 60% likely to be a peanut. Unless rotteness was one of your selection critereon when you grabbed the nut.

Answer 3

ok first you take the probability of it being a peanut, 60%. now you take the probability of it being not rotten, 55%. turn the percentages into decimals, so 0.6 and 0.55. multiply them and you get 0.33 or 33%.

so the answer is 33% or 33/100

vote mine best

Answer 4

Probabilities:

/ almond (0.4)
___/ salted (0.45)
______/ rotten (0.05/(0.4*0.45)=0.278)
______\ !rotten (1-0.05/(0.4*0.45)=0.722)
___\ unsalted (1-0.45=0.55)
______/ rotten (1-0.08/(0.4*0.55)=0.64)
______\ !rotten (0.08/(0.4*0.55)=0.36)
\ peanut (1-0.4=0.6)
___/ salted (0.65)
______/ rotten (0.45)
______\ !rotten (0.55)
___\ unsalted (1-0.65=0.35)
______/ rotten (0.45)
______\ !rotten (0.55)

find P(peanut | !rotten)

P(rotten | peanut) = 0.45 given
therefore P(!rotten | peanut) = 0.55

P(peanut | !rotten) = P(!rotten | peanut)*P(peanut)/P(!rotten)

P(!rotten | peanut) = 0.55
P(peanut) = 0.6
P(!rotten) =
0.6*0.65*0.55
+0.6*0.35*0.55
+0.4*0.45*0.722
+0.4*0.55*0.36 = 0.54

therefore P(peanut | !rotten) = 0.61