A locker combination has three nonzero digits, and digits cannot be repeated. If the first two digits are even, what is the probability that the third digit is even?
Assuming that the combination choices consist of single digits,
and we have only 4 even digits (2,4,6,8) where 2 are already used up,
we only have 2 out of 7 to pick from
so prob(your event) = 2/7
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To find the probability that the third digit is even given that the first two digits are even, we can first determine the total number of possible combinations with three nonzero digits.
Step 1: Find the total number of ways to choose the first digit:
Since the first digit should be nonzero and even, we have 4 choices (2, 4, 6, or 8).
Step 2: Find the total number of ways to choose the second digit:
Since the second digit also needs to be even and different from the first digit, we have 3 choices left (2 choices if the first digit is already chosen).
Step 3: Find the total number of ways to choose the third digit:
Since the third digit cannot be zero, it has 8 possible choices (1 to 9, excluding the first two digits already chosen). Out of these 8 choices, half are even (2, 4, 6, 8).
Now, we can calculate the probability:
Step 4: Calculate the total number of possible combinations:
The total number of possible combinations is the product of the choices from each step: 4 choices for the first digit, multiplied by 3 choices for the second digit, multiplied by 8 choices for the third digit. Therefore, the total number of possible combinations is 4 * 3 * 8 = 96.
Step 5: Calculate the number of combinations with an even third digit:
Out of the 8 choices for the third digit, 4 are even. Therefore, the number of combinations with an even third digit is 4.
Step 6: Calculate the probability:
The probability is the number of favorable outcomes (combinations with an even third digit) divided by the total number of possible outcomes (total combinations). So, the probability is 4 (even third digit) / 96 (total combinations) = 1/24.
Therefore, the probability that the third digit is even given that the first two digits are even is 1/24.