Question

A,b, c chosen randomly and with replacement from the set {1,2,3,4,5}, the probability that a * b + c is even.

Answer 1

https://artofproblemsolving.com/wiki/index.php?title=1995_AHSME_Problems/Problem_20

refer this

Answer 2

Answer:

$\frac{59}{125}$

Step-by-step explanation:

Given sets,

{1, 2, 3, 4, 5},

∵ a * b + c = even are,

Case 1 :

a*b = even and c = even

If a*b = even ⇒ a = even or b = even,

a = 1, b = 2, 4, ( 2 possible ways )

a = 2, b = 1, 2, 3, 4, 5, ( 5 possible ways )

a = 3, b = 2, 4 ( 2 possible ways )

a = 4, b = 1, 2, 3, 4, 5 ( 5 possible ways )

a = 5, b = 2, 4 ( 2 possible ways )

Now, c = even = 2, 4 ( 2 possible ways )

So, the total ways = 16 × 2 = 32

Case 2 :

a*b = odd and c = odd

a = 1, 3, 5 ( 3 possible ways ),

b = 1, 3, 5, ( 3 possible ways )

c = 1, 3, 5 ( 3 possible ways )

So, the total ways = 3 × 3 × 3 =27

Thus, the total possible ways for which a*b + c is even = 32 + 27 = 59

Now, the total ways of selecting any three numbers from the given set = 5 × 5 × 5 × 5 × 5 = 125,

Hence, the probability that a * b + c is even = $\frac{59}{125}$