Question

If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set (5, 6, 7), what is the probability that xy will be even?

Answer 1

Step-by-step explanation:

for xy to be even, either both of them should be even or one should be odd and other even:

CASE 1 : WHEN BOTH ARE EVEN

let A be event that x is even

then P(A)=2/4=1/2

( THERE ARE ONLY TWO EVEN NOS. IN GIVEN SET OF X)

probability of y to be even:

let B be an event that y is even

then P(B)=1/3

then probability that xy is even

P(A)×P(B)=1/2×1/3=1/6 ..... (1)

CASE 2: WHEN X IS EVEN AND Y ODD

P(A)=2/4=1/2

let e be event that y is odd

P(e)=2/3

probability that xy is even:

P(A)×P(e)=1/2×2/3=1/3 (2)

CASE 3:WHEN X IS ODD AND Y EVEN

let a be event that x is odd

P(a)=2/4=1/2

P(B)=1/3

probability of xy to be even ( x is odd ,y even)

1/2×1/3=1/6 (3)

REQUIRED PROBABILITY ( add 1,2 and 3)

=1/6+1/3+1/6

=2/3