If an event has a 55% chance of happening in one trial, how do I...

matt roberts

matt roberts

Answered

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

Ian Adams

Expert

2022-07-28Added 101 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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