The probability that exactly 4 are cured from 7 dolphins is 0.0128
<h3>What is Probability ?</h3>
Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
![P = ^nC_r p^r q^{n-r}](https://tex.z-dn.net/?f=P%20%3D%20%5EnC_r%20p%5Er%20q%5E%7Bn-r%7D)
Putting the values
![P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}](https://tex.z-dn.net/?f=P%20%3D%20%5E7C_4%20%28%5Cdfrac%7B92%7D%7B100%7D%29%5E4%20%28%5Cdfrac%7B8%7D%7B100%7D%29%5E%7B7-4%7D)
![P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}](https://tex.z-dn.net/?f=P%20%3D%20%5Cdfrac%7B7%21%7D%7B4%21%20%5C%3B3%21%7D%20%28%5Cdfrac%7B92%7D%7B100%7D%29%5E4%20%28%5Cdfrac%7B8%7D%7B100%7D%29%5E%7B7-4%7D)
P = 0.0128
Therefore the probability is 0.0128.
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