Final answer:
The probability that a signal is a two-flag message is calculated by dividing the number of two-flag combinations by the total number of potential signals. With 4 two-flag combinations and 12 total signals possible, the probability is 1/3 , option d).
Step-by-step explanation:
The question pertains to probability and involves finding the chance that a two-flag signal is displayed using the available flags. To determine this, we need to count the number of possible two-flag combinations that can be arranged and then divide that by the total number of ways to display any number of flags.
Since there are six flags in total (3 blue, 2 yellow, 1 red), let's enumerate the possible signals. For two-flag signals, we don't distinguish between the order—they will be considered the same regardless of which is on top. Considering the identical nature of the blue and yellow flags, the possible two-flag combinations are blue-blue, blue-yellow, blue-red, and yellow-red. That gives us a total of 4 different two-flag signals. Now we need to find the total number of possible signals regardless of the length. Since we can use from one to six flags, we should calculate the sum of the combinations for each possible signal length:
1-flag signals: 3 (blue, yellow, red)
2-flag signals: 4 (as calculated above)
3-flag signals: 3 (blue-blue-yellow, blue-blue-red, blue-yellow-red)
4-flag signals: 1 (blue-blue-yellow-red)
5-flag signals: 0 (not possible with the available flags)
6-flag signals: 1 (all flags, but only in one way since the blues and yellows are identical)
Adding these up gives us a total of 3 + 4 + 3 + 1 + 0 + 1 = 12 possible signals.
The probability that a signal is a two-flag message is then the number of two-flag combinations divided by the total number of signals, which is 4/12 or 1/3. Therefore, the answer is (d) 1/3.