If an event has a 55% chance of
matt roberts
Answered question
2022-07-28
If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?
Answer & Explanation
Ian Adams
Skilled2022-07-28Added 140 answers
Given -
Chance of happening of an event in one trial = 55%
To Find -
Chances of it happening more than once in 4 trials =?
Step-by-Step Explanation -
Probability (Happening) = 55% or 0.55
Probability (Not Happening) = 45% or 0.45
Now,
Chances of it happening more than once in 4 trials =
It can happen for 2, 3 or 4 times.
So the cases are:
HHNN = 0.55×0.55×0.45×0.45 = 0.06125
Also, the number of ways it can be done = ⁴C₂ = 4!/(2!)(4 - 2)! = (4×3×2×1)/(2×1)(2×1)
= 3×2 = 6
= 6×0.06125
= 0.3675
Also, the number of ways it can be done = ⁴C₂ = 4!/(2!)(4 - 2)! = (4×3×2×1)/(2×1)(2×1)
= 3×2 = 6 = 0.0748
The number of ways it can be done = ⁴C₃ = 4!/(3!)(4 - 3)! = (4×3×2×1)/(3×2×1)(1)
= 4
= 4× 0.0748
= 0.2992
= 6×0.06125
= 0.367555 = 0.0915
The number of ways it can be done = 1
So,
Total = 0.3675 + 0.2992 + 0.0915 = 0.7582 or 75.82%
Final Answer -
Chances of it happening more than once in 4 trials = 0.7582 or 75.82%
HHHN = 0.55×0.55×0.55×0.45 = 0.0748
The number of ways it can be done = ⁴C₃ = 4!/(3!)(4 - 3)! = (4×3×2×1)/(3×2×1)(1)
= 4
= 4× 0.0748
HHHH = 0.55×0.55×0.55×0.55 = 0.0915
{Where H =Happening, N = Not Happening}
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