Two brothers enter a race with 5 others. Racers draw names to determine their starting positions (1 to 6). What's the probability that the older brother will start in lane 1 with his brother directly beside him?
There is a 1-in-6 chance the eldest gets lane 1 and a 1-in-5 chance the younger gets lane 2. (1/6)*(1/5)=
To calculate the probability that the older brother will start in lane 1 with his brother directly beside him, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
There are 6 racers in total, and each racer can start in any of the 6 lanes. Therefore, the total number of possible outcomes is 6 * 5 * 4 * 3 * 2 * 1 = 720 (since there are 6 choices for the first racer, 5 for the second, and so on).
Number of favorable outcomes:
For the older brother to start in lane 1 with his brother directly beside him, there are two scenarios:
1. The older brother starts in lane 1, and the younger brother starts in lane 2.
2. The younger brother starts in lane 1, and the older brother starts in lane 2.
For each of these scenarios, the remaining racers can start in any of the remaining 4 lanes, so there are 4! = 4 * 3 * 2 * 1 = 24 ways to arrange them.
Therefore, the number of favorable outcomes is 2 * 24 = 48.
Probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 48 / 720
Probability = 1 / 15
So, the probability that the older brother will start in lane 1 with his brother directly beside him is 1/15 or approximately 0.0667 (rounded to four decimal places).