Question 1144391: In a neighborhood, 80% of the families have a vegetable garden, and 25% have a vegetable garden and grow lettuce in it. Find the probability that if we select a family from those known to have a vegetable garden, they will grow lettuce in it.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
It is about so called "conditional probability".
If A and B are events, the conditional probability P(A | B) //probability of A under the condition B// is defined in this way
P(A | B) = P(A and B) / P(B).
P(A and B) is the probability of the event (A and B).
In your case
event A is "family has a vegetable garden";
event B is "family grows lettuce in the garden";
event (A and B) = "family has a vegetable garden and grow lettuce in it".
You are given P(A) = 0.8; P(A and B) = 0.25, and they ask you about P(A | B).
According to the definition, P(A | B) = P(A and B) / P(B) =  = 0.3125.
ANSWER. the probability that if we select a family from those known to have a vegetable garden, they will grow lettuce in it is 0.3125.
When the beginners start solving such problem, the most difficult part for them is to understand who is (A and B).
As soon as the student will get who is (A and B) (and who are A and B separately), the solution becomes OBVIOUS.
On intuitive level, now you should relate 0.25 of the total population not to all population, but only to 0.8 part of it.
But the key to success is to firmly know the definition of the conditional probability via an intersection.
--------------
For more help, and to see other similar solved problems, see the lesson
- Conditional probability problems
in this site.
|
|
|
