Answer :
Using the binomial probability principle, the probability of selecting two left-handed people at random is 0.0486.
What is binomial probability?
In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).
The binomial probability is nCx⋅px⋅(1−p)n−x if the likelihood of success on a given trial is p.
For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail.
A binomial probability distribution is another name for this distribution.
So, regarding a binomial distribution:
P(x = x) = nCx * p^x * q^(n-x)
Probability, p = 0.10
q = 1 - p = 1 - 0.10 = 0.90
and n = 4 trials.
Now, calculate as follows:
P(x = 2) = 4C2 × 0.10² × 0.90²
P(x = 2) = 6 × 0.01 × 0.81
P(x = 2) = 0.0486
Therefore, using the binomial probability principle, the probability of selecting two left-handed people at random is 0.0486.
Know more about binomial probability here:
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Correct question:
A small college has 800 students, 10%, percent of which are left-handed. Suppose they take an SRS of 444 students. Let X= equal the number of left-handed students in the sample.
What is the probability that exactly 2 of the 4 students are left-handed?
You may round your answer to the nearest hundredth.
