Final answer:
The probability of rolling an odd number on a specially weighted die where the number 4 appears twice as often as any other number is 3/7, since there are 3 occurrences of odd numbers and 7 total possible outcomes.
Step-by-step explanation:
The question asks about the probability that a specially weighted die will land on an odd number, with the number 4 appearing twice as often as each other number. First, let's determine the total number of possible outcomes. Normally, a six-sided die would have 6 equally likely outcomes, but given that the number 4 is twice as likely, we consider it as having two 'chances'. Thus, the total number of possible outcomes is 1 + 1 + 1 + 2 + 1 + 1 = 7.
Next, we need to count the number of favorable outcomes for rolling an odd number. On a standard die, the odd numbers are 1, 3, and 5, each occurring once. Therefore, the number of occurrences of odd numbers is 1 (for 1) + 1 (for 3) + 1 (for 5) = 3.
To find the probability of rolling an odd number, divide the number of favorable outcomes by the total number of outcomes: P(odd) = 3/7. So, the correct answer is D. 3/7.