A number is randomly selected from the set of numbers 1 through 26. Find the probability of selecting an even number given that the outcome is a number less than 16.
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TOTAL NO. OF POSSIBLE OUTCOME= 26
FAVORABLE OUT COME 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
NUMBER OF FAVORABLE= 13
P(GETTING AN EVEN NUMBER)=13/26
HENCE PROBABILITY OF EVEN NUMBERS IS 1/2
FAVORABLE OUT COME 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
NUMBER OF FAVORABLE= 13
P(GETTING AN EVEN NUMBER)=13/26
HENCE PROBABILITY OF EVEN NUMBERS IS 1/2
TPS:
It's wrong. You missed the last condition.
WT
OK
:)
:P
Answered by
5
Let A be the event ‘the number selected is even’
B be the event ‘the number selected is less than 16’.
We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6,....., 26}
Then A = {2, 4, 6,.....,24, 26}, B = {1, 2 ,3 , 4, 5 , ....., 15}
and A ∩ B = {2, 4, 6, 8, 10, 12, 14}
P(A) = 13/26 , P(B) = 15/26, P(A ∩ B) = 7/26
P(A|B) =P(A ∩ B)/ P(B) = 7/15
B be the event ‘the number selected is less than 16’.
We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6,....., 26}
Then A = {2, 4, 6,.....,24, 26}, B = {1, 2 ,3 , 4, 5 , ....., 15}
and A ∩ B = {2, 4, 6, 8, 10, 12, 14}
P(A) = 13/26 , P(B) = 15/26, P(A ∩ B) = 7/26
P(A|B) =P(A ∩ B)/ P(B) = 7/15
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