matt roberts

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?

Expert

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%

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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