Final answer:
The probability that a two-digit number formed from the digits 1, 3, 4, 6 is divisible by 4 is 3/16, as there are 3 such numbers (16, 36, 64) out of a total of 16 possible combinations.
Step-by-step explanation:
To find the probability that a two-digit number formed from the digits 1, 3, 4, 6 is divisible by 4, we first establish the sample space S. Since repetition of the digits is allowed, the total number of different two-digit numbers that can be formed is 4 × 4 = 16 (i.e., there are four choices for the tens place and four choices for the ones place). Thus, n(S) is 16, representing all possible two-digit combinations of the digits 1, 3, 4, and 6.
For a number to be divisible by 4, the last two digits (tens and ones place) of the number must be divisible by 4. We need to list out all combinations where the two-digit number meets this criterion to find event A. The valid combinations that are divisible by 4 would be 16, 36, and 64 (since 14 and 34 are not divisible by 4). Therefore, n(A) is 3, as there are three outcomes where a number formed from the chosen digits is divisible by 4.
The probability P(A) that the number formed is divisible by 4 is the ratio of the number of favorable outcomes to the total number of possible outcomes, which is n(A) / n(S) = 3 / 16.