he correct answerA basketball game is played between team Blue and Red. There are a total of 9 players in each them and 5 will play in the game. Ankit is in team blue and Vaibhav is in team Red. What is the probability that at least one of ankit or vaibhave is in playing five?Options125/15356/8165/8172/81
Question
he correct answerA basketball game is played between team Blue and Red. There are a total of 9 players in each them and 5 will play in the game. Ankit is in team blue and Vaibhav is in team Red. What is the probability that at least one of ankit or vaibhave is in playing five?Options125/15356/8165/8172/81
Solution
The problem can be solved by calculating the probability that neither Ankit nor Vaibhav is playing, and then subtracting this from 1.
Step 1: Calculate the probability that Ankit is not playing. There are 9 players in team Blue and 5 are chosen to play. The number of ways to choose 5 players out of 9 is "9 choose 5", which equals 126. The number of ways to choose 5 players out of the 8 remaining (excluding Ankit) is "8 choose 5", which equals 56. So, the probability that Ankit is not playing is 56/126 = 4/9.
Step 2: Calculate the probability that Vaibhav is not playing. Similarly, the probability that Vaibhav is not playing is also 4/9.
Step 3: Calculate the probability that neither Ankit nor Vaibhav is playing. The events that Ankit is not playing and Vaibhav is not playing are independent, so the probability that neither is playing is the product of their individual probabilities: (4/9) * (4/9) = 16/81.
Step 4: Calculate the probability that at least one of Ankit or Vaibhav is playing. This is 1 minus the probability that neither is playing: 1 - 16/81 = 65/81.
So, the correct answer is 65/81.
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