Help with conditional probability

[imjello]

A number is selected randomly from a container containing all the integers from 10 to 50 find

a) p(even|greater than 40)
b) p(greater than 40| even)
c) p(prime| between 20 and 40)

please provide an explanation, thanks a lot =D

 

[imjello]

Idk if people haven't answered because i didn't show work or not but there isn't much work to show in the first place here's what i tried anyway.

a. probability its even .5 (5/10)/ probability its greater than 40(1/5) .2 = 2.5 which is over one so obviously wrong

b. probability its greater than 40(1/5) .2 / .5= .4

c. (26/50).52/ (20/50) .4 = 1.3 once again over one

i feel stupid for not understanding how to do these i understand when its in a chart but can't get these question

 

[A. Bahat]

I'll give an example: say we wanted to find P(odd | less than or equal to 20). This probability is just the proportion of numbers between 10 and 20 (inclusive) that are odd. These numbers are 11,13,15,17,19; there are 5 of them out of 11 choices, so the the probability sought is 5/11.

 

[eumyang]

a. probability its even .5 (5/10)/ probability its greater than 40(1/5) .2 = 2.5 which is over one so obviously wrong

Looks like you're thinking that
P(even|greater than 40) = \frac{P(\text{even})}{P(\text{> 40})}
... and that is wrong. It should be
P(even|greater than 40) = \frac{P(\text{even AND > 40})}{P(\text{> 40})}
Try it again.

b. probability its greater than 40(1/5) .2 / .5= .4

Nope. Like in part a, the setup would be
P(greater than 40| even) = \frac{P(\text{> 40 AND even})}{P(\text{even})}

 

[HallsofIvy]

A number is selected randomly from a container containing all the integers from 10 to 50 find

a) p(even|greater than 40)

There are 10 numbers in the container that are larger than 40. How many of them are even?

b) p(greater than 40| even)

There are 21 numbers in the container that are even. How many of them are greater than 40?

c) p(prime| between 20 and 40)

There are 19 numbers in the container between 20 and 40. How many of them are prime?
(I am assuming that "between 20 and 40" means 21 to 39.

please provide an explanation, thanks a lot =D