The probability of having 1 girl and 3 boys is 0.25 or 25%. Computed using Binomial distribution.
The probability of an event is the ratio that determines the chance of occurrence of that event.
If A is an event, n is the number of favorable outcomes to event A, and S is the total number of possible outcomes in the experiment, then the probability of event A is given as:
P(A) = n/S.
Binomial distribution is the probability that precisely x successes will occur on n subsequent trials with p probability, as determined by:
P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.
nCx is determined by how many possible ways there are to combine x items from a collection of n components, and is given as:
nCx = n!/{x!(n - x)!}.
In the question, we are asked to find the probability of having 1 girl and 3 boys in a 4-child family.
The probability of having a girl and a boy is equally likely.
Assuming the event of having a girl as success, we can design a binomial distribution with p = 0.5, q = 1 - p = 0.5, and n = the number of children = 4.
Thus, the probability of having 1 girl and 3 boy, can be shown as:
P(x = 3) = 4C3(0.5)¹(0.5)⁴⁻¹,
P(x = 3) = 4C3(0.5)¹(0.5)³,
or, P(x = 3) = 4*0.5*0.125,
or, P(x = 3) = 0.250 or 25%.
Thus, the probability of having 1 girl and 3 boys is 0.25 or 25%. Computed using Binomial distribution.
Learn more about binomial distribution at
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