JEE Main 2024 Mathematics question
In a tournament, a team plays 10 matches with probabilities of winning and losing each match as and respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P(|x − y| ≤ 2) is p, then 3⁹p equals……
Answer: 8288
Solution
x + y = 10, so |x − y| ≤ 2 means x = 4, 5, 6. Then 3¹⁰p = C(10,4)2⁶ + C(10,5)2⁵ + C(10,6)2⁴ = 13440 + 8064 + 3360 = 24864, and 3⁹p = 8288.