Eight men enter a doubles tennis tournament in which partners are selected by lot. What is the probability that two brothers, Sean and Kevin, will be selected as partners?
there are 7 times Sean and Kevin have the probability to be selected as partners.
To find the probability that Sean and Kevin will be selected as partners, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since there are 8 men, the first person can be assigned a partner in 7 ways. After this pairing, the remaining 6 men can form pairs in (6 choose 2) ways. Therefore, the total number of outcomes is:
7 * (6 choose 2) = 7 * (6! / (2! * (6-2)!)) = 7 * (6! / (2! * 4!)) = 7 * (6 * 5) / (2 * 1) = 7 * 15 = 105
Number of favorable outcomes:
Since Sean and Kevin are brothers, the first person can be assigned a partner in 1 way. After this pairing, the remaining 6 men can form pairs in (6 choose 2) ways. Therefore, the number of favorable outcomes is:
1 * (6 choose 2) = 1 * (6! / (2! * (6-2)!)) = 1 * (6! / (2! * 4!)) = 1 * (6 * 5) / (2 * 1) = 6 * 5 = 30
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of outcomes
= 30 / 105
= 2 / 7
Therefore, the probability that Sean and Kevin will be selected as partners is 2/7.
To find the probability that two specific individuals, Sean and Kevin, will be selected as partners in the doubles tennis tournament, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When randomly selecting partners for a doubles tournament, each player can be paired with any of the remaining players. The first player has 7 possible partners, the second player has 6 possible partners (excluding the first player and himself), the third player has 5 possible partners, and so on. Hence, the total number of possible outcomes is given by 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 (since there are 8 players in total).
Number of favorable outcomes:
In order for Sean and Kevin to be partners, we can treat them as one unit in the pairing process. So, there are effectively 6 individuals remaining to be paired with the Sean-Kevin unit. Each of these 6 individuals can be paired with Sean-Kevin, giving us a total of 6 possible partnerships.
Therefore, the number of favorable outcomes is 6.
Probability:
The probability of an event occurring is defined as the number of favorable outcomes divided by the number of possible outcomes. Therefore, the probability that Sean and Kevin are selected as partners is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 5040
≈ 1/840 or approximately 0.00119
So, the probability that Sean and Kevin are selected as partners in the doubles tennis tournament is approximately 1/840 or 0.00119.