Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .
10% of the people experiences dizziness.
Probability that a random patient experiences dizziness = 0.1
Probability that the person does not experience dizziness = 0.9
Now this is in the form of a binomial distribution such that the probability is given by:
Sample = 15
P = 0.1
P' =0.9
Required probability :
= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)
= 1 × 0.1⁰ × 0.9¹⁵
= 0.20589...
≈ 0.206
Hence the required probability is approximately 0.206 .
The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.
If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.
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