a basketball game is played between two teams blue and red there are a total of 10 players in each team and 6 will play the game. jimmy is in the team blue and crane is in the team red what is the probability that at least one of jimmy or crane is in playing field
Answers
Given : a basketball game is played between two teams blue and red there are a total of 10 players in each team and 6 will play the game. jimmy is in the team blue and crane is in the team red
To Find : the probability that at least one of jimmy or crane is in playing field
Solution:
There are 10 players in each team
Number of way Each team can be selected = ¹⁰C₆ = 210
Total Ways = 210 * 210
jimmy is selected = 1 * ⁹C₅ = 126 ways
Jimmy is not selected = ⁹C₆ = 84 ways
Same for crane
crane is selected = 1 * ⁹C₅ = 126 ways
crane is not selected = ⁹C₆ = 84 ways
at least one of jimmy or crane is in playing field
jimmy is selected * crane is not selected + Jimmy is not selected * crane is selected + jimmy is selected * crane is selected
= 126 * 84 + 84 * 126 + 126 * 126
= 126 * ( 84 + 126 + 126)
= 126 * ( 336)
Probability that at least one of jimmy or crane is in playing field
= 126 * ( 336) / ( 210 * 210)
= 0.96
0.96 is the probability that at least one of jimmy or crane is in playing field
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