In a set of 6 numbers, {-2, -1, 0, 1, 2, 3}, what is the probability the product of any two numbers is zero?
It is the same as saying that a 0 is picked, either as 1st or 2nd pick:
(1/6)(1) + (5/6)(1/5) = 1/3
maybe:
same as the probability that one of the numbers you choose is zero probability that first one is zero = 1/6
probability that second one is zero also is 1/6
so sum is 2/6 = 1/3
To find the probability that the product of any two numbers in the set is zero, we first need to determine the total number of pairs we can form and then count the number of pairs whose product is zero.
The set has 6 numbers: {-2, -1, 0, 1, 2, 3}. The total number of pairs we can form is given by the combination formula, which is nCr (n Choose r), where n is the total number of elements and r is the number of elements we choose from the set to form a pair.
In this case, we want to choose 2 numbers from the set, so n = 6 and r = 2. Therefore, the total number of pairs we can form is:
nCr = 6C2 = 6! / (2!(6-2)!) = 6! / (2!4!) = (6 * 5) / (2 * 1) = 15
Now we need to determine the number of pairs whose product is zero. Since zero multiplied by any number is always zero, we need to count the occurrences of zero in the set.
In this case, there is only one occurrence of zero. Therefore, there is only one pair whose product is zero, which is (0, 0).
So, the probability that the product of any two numbers in the set is zero is:
Number of pairs with product zero / Total number of pairs
1 / 15
Hence, the probability is 1/15.