Probability that the product is even

[Zelda22]

From each of the three boxes below, one number is chosen at random and the three numbers are then multiplied together. What is the probability that the product is even?

box 1 : 2,3,4,5
box 2 : 4,5,6,7
box 3: 1,2,5,8,10

p( 3 even 0 odd),(2 even 1 odd),(1 even 2 odd )

Can I use complement??
the events include 0 odd, 1 odd, and 2 odd. (But not 3 odd)

3 odd = 1/2* 1/2* 2/5
= 1/10

1- (3 odd)
1- 1/10 = 9/10
-----------------------------
3 even 0 odd
even * even * even = even
1/2 * 1/2 * 3/5 = 3/20

2 even 1 odd = even
even * even * odd = 1/2 * 1/2 * 2/5= 2/20 = 1/10
odd * even * even = 1/2 * 1/2 * 3/5= 3/20
even * odd * even= 1/2 * 1/2 *3/5= 3/20

1/10 + 3/20 + 3/20 = 2/5

1 even 2 odd = even
even * odd * odd= 1/2 * 1/2 * 2/5 = 1/10
odd * odd * even = 1/2 * 1/2 * 3/5 = 3/20
odd * even * odd= 1/2 * 1/2 * 2/5 = 1/10

1/10 + 3/20 + 1/10 = 7/20

p (n*n*n= even) =( 3 even 0 odd),(2 even 1 odd),(1 even 2 odd )
3/20 + 2/5 + 7/20 = 9/10

 

[BigBeachBanana]

From each of the three boxes below, one number is chosen at random and the three numbers are then multiplied together. What is the probability that the product is even?

box 1 : 2,3,4,5
box 2 : 4,5,6,7
box 3: 1,2,5,8,10

p( 3 even 0 odd),(2 even 1 odd),(1 even 2 odd )

Can I use complement??
the events include 0 odd, 1 odd, and 2 odd. (But not 3 odd)

3 odd = 1/2* 1/2* 2/5
= 1/10

1- (3 odd)
1- 1/10 = 9/10
-----------------------------
3 even 0 odd
even * even * even = even
1/2 * 1/2 * 3/5 = 3/20

2 even 1 odd
even * even * odd = 1/2 * 1/2 * 2/5= 2/20 = 1/10
odd * even * even = 1/2 * 1/2 * 3/5= 3/20
even * odd * even= 1/2 * 1/2 *3/5= 3/20

1/10 + 3/20 + 3/20 = 2/5

1 even 2 odd
even * odd * odd= 1/2 * 1/2 * 2/5 = 1/10
odd * odd * even = 1/2 * 1/2 * 3/5 = 3/20
odd * even * odd= 1/2 * 1/2 * 2/5 = 1/10

1/10 + 3/20 + 1/10 = 7/20

p( 3 even 0 odd),(2 even 1 odd),(1 even 2 odd )
3/20 + 2/5 + 7/20 = 9/10

Looks good. You can also do the complement of getting no even number from 3 boxes.

 

[Zelda22]

Thank you.