0, 5, 10, 12 what is the probability the product is zero?

Answer 1

One way to approach this problem would be to think of the total number of ways that the product could be 0, and then divide that by the total number of possible products.

(Total number of products that equal 0) / (Total Number of Products) = (Probability that a randomly chose product equals 0)

Because multiplication is commutative, we know that the order does not matter when multiplying two given numbers. Hence, we can find the total number of Products by using the formula for combinations

Total combinations = n! / (n-r)!r!

[where n is the total amount of numbers, and r is the amount of numbers we are choosing]

So, (Total Number of Products) = 4! / 2!2! = 24 / 4 = 6

Now, how many of these products are equal to 0? We can deduce that the only products that equal 0 will be the products that include the number 0. So, we will have exactly 3 products equaling 0. (0x5, 0x10, and 0x12)

Therefore,

(Probability that a randomly chose product equals 0) = 3 / 6 = 1 / 2 = 50%