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Question
Two-digit numbers are formed from the digits 0,1,2,3,4 where digits are not repeated. Find the probability of the events that:
(a) The number formed is an even number.
(b) The number formed is a prime number.
Solution
The digits given are 0,1,2,3,4
∵ The digits are not repeated
∴ we can form two digits numbers in the sample space
Sample Space
S ≡ {10 , 12 , 13 , 14 , 20 , 21 , 23 , 24 , 30 , 31 , 32 , 34 , 40 , 41 , 42 , 43}
∴ n(S) = 16
(a) Let A ≡ Event of getting an even number
A ≡ {10 , 12 , 14 , 20 , 24 , 30 , 32 , 34 , 40 , 42}
n(A) = 10
P(A) = `("n"("A"))/("n"("S")) = 10/16`
P(A) = `5/8`
(b) Let B ≡ Event of getting a prime number
B ≡ {13 , 23 , 31 , 41 , 43}
n(B) = 5
P(B) = `"n(B)"/"n(S)" = 5/16`
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