Question 1087704: An experimental serum was injected into 500 guinea pigs initially 150 of the guinea pigs had circular cells 250 had elliptical cells and 100 had irregular cells after the serum was injected 25 of the guinea pigs with circular cells were affected 200 with elliptical cells were affected and 0 of those with irregular cells were affected find the empirical probability that a guinea pig with elliptical cells were affected by injection of the serum.
Thank you!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Problem:
An experimental serum was injected into 500 guinea pigs. Initially 150 of the guinea pigs had circular cells, 250 had elliptical cells, and 100 had irregular cells. After the serum was injected, 25 of the guinea pigs with circular cells were affected, 200 with elliptical cells were affected, and 0 of those with irregular cells were affected. Find the empirical probability that a guinea pig with elliptical cells were affected by injection of the serum.
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Work Shown:
Define two events E and S where
E = guinea pig has elliptical cells
S = guinea pig's cells is affected by the serum
------------------------------
P(E) = probability of selecting guinea pig with elliptical cells
P(E) = (number of guinea pigs with elliptical cells)/(number of guinea pigs total)
P(E) = 250/500
P(E) = 0.5
------------------------------
P(S and E) = probability of having cells affected by serum AND guinea pig has elliptical cells
P(S and E) = (number of guinea pigs with elliptical cells affected by serum)/(number of guinea pigs total)
P(S and E) = 200/500
P(S and E) = 0.4
------------------------------
We're told to "Find the empirical probability that a guinea pig with elliptical cells were affected by injection of the serum", which means that we're given the guinea pig has elliptical cells.
We want to use this known given info to find the probability of event S occurring.
In conditional probability notation, this means we want to find P(S|E). Asking "What is the value of P(S|E)?" is basically the same as asking "What is P(S) given we know E happened?"
Use the formula below and plug in the values we found earlier
P(S|E) = P(S and E)/P(E)
P(S|E) = 0.4/0.5
P(S|E) = 4/5
P(S|E) = 0.8
P(S|E) = 80%
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Answer in fraction form: 4/5
Answer in decimal form: 0.8
Answer in percent form: 80%
The three answers are equivalent to each other just written in different forms.
|
|
|
