Question

In one jar, I have two balls labelled 1 and 2 respectively. In a second jar, I have three balls labelled 0, 1 and 2 respectively. I draw one ball from each jar, multiply the numbers on the two balls together, and then calculate three to the power of that product, e.g. if I draw 1 and 2, I calculate 3^2=9. Let’s call this number X. What is the probability that the number 1,024 is an exact multiple of X?

Answer 1

Step-by-step explanation:

this is a kind of trick question, actually.

with whatever we draw, we produce X values as power of 3.

to be precise, we can have only

3⁰ = 1

3¹ = 3

3² = 9

3⁴ = 81

due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).

so, mostly, these results cannot be exact factors of 1024.

1024 cannot be divided by 3, nor by 9 nor by 81.

but 1024 is a multiple of 1 (as is every number).

so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.

the only possibilities are

1 and 0

2 and 0

out of in total 6 (2×3) different outcomes

1 and 0

1 and 1

1 and 2

2 and 0

2 and 1

2 and 2

the probability of this "0" event is again

number of desired outcomes / number of possible outcomes = 2/6 = 1/3