Final answer:
The probability of selecting a number between 1 and 10 that is a factor of both 4 and 6 is 1/5, since the only common factors within this range are 1 and 2.
Step-by-step explanation:
A number is chosen from 1-10. To find the probability of selecting factors of 4 and factors of 6, we first need to identify these factors within the range of 1 to 10. The factors of 4 are 1, 2, and 4. The factors of 6 are 1, 2, 3, and 6. However, only the common factors of both 4 and 6 are relevant for this probability, which are 1 and 2.
As there are two favorable outcomes and ten possible outcomes total, the probability of selecting a number that is a factor of both 4 and 6 is calculated by dividing the number of favorable outcomes by the total number of outcomes. Therefore, the probability is 2/10 which simplifies to 1/5 or 0.2.