In a random sample of 5 infants affected by tetanus, the probability that only two will recover is 7.29%.
In a binomial distribution, the probability of getting a success must remain the same for the trials we are investigating.
For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
The formula for binomial probability is;
P(X = x) = ⁿCₓ * p^(x) * (1 - p)^(n - x)
where;
p is probability of success
q = 1 - p is probability of failure
n is sample size
x is number of successes
We are given;
p = 10% = 0.1
n = 5
x = 2
Thus;
P(X = 2) = ⁵C₂ * 0.1² * (1 - 0.1)⁵ ⁻ ²
P(X = 2) = 0.0729
P(X = 2) = 7.29%
Thus, in a random sample of 5 infants affected by tetanus, the probability that only two will recover is 7.29%
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