The probability of winning a prize in a game of chance is 0.48. What is the least number of games that must be
played to ensure that the probability of winning at least twice is more than 0.95?
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Answer:
8 number of games
Step-by-step explanation:
The probability of winning a prize in a game of chance is 0.48
Probability of loosing / Not winning = 1 - 0.48 = 0.52
Let say n games to be Played
winning at least twice means = 1 - winning 0 time - winning 1 time
= 1 - ⁿC₀(0.48)⁰(0.52)ⁿ - ⁿC₁(0.48)¹(0.52)ⁿ⁻¹ > 0.95
=> ⁿC₀(0.48)⁰(0.52)ⁿ + ⁿC₁(0.48)¹(0.52)ⁿ⁻¹ < 0.05
=> (0.52)ⁿ + n(0.48)(0.52)ⁿ⁻¹ < 0.05
=> (0.52)ⁿ⁻¹(0.52 + 0.48n) < 0.05
=> n = 8
8 number of games must be played to ensure that the probability of winning at least twice is more than 0.95
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