Answer to Question #252140 in Statistics and Probability for clarktzy

Question

Eight students attended a birthday party: Three * (3) of them confirmed Couid d - 10 positive. The contact tracer bad conducted rondom. test for only two students. Find the probabi lity distribution for random variable & which represents the number of Covid-1a positive patients. Now, think of three stedements of the problem out of the topic "Covid-19?"

Answer 1

This scenario can be described by a binomial distribution because the experiment results in an outcome that can be classified as either a success or failure. For this case, the test results in either a student being Covid-19 positive(success) or Covid-19 negative(failure).

Let $X$ be a random variable representing the number of Covid-19 patients, $n$ be the number of trials, $x$ be the number of successes out of $n$ trials and $p$ be the probability of success.

Therefore, out of $n=8$ students, the number of successes are $x=3$ and the probability of success $p=(x/n)=3/8$. The probability of failure is given as $q=1-p=1-3/8=5/8$ .

The probability distribution of the random variable $X$ is given by the formula,

$p(X=x)=\binom{8}{x}p^x(1-p)^{n-x},\space x=0,1,2,3,4,5,6,7,8$

$0,\space elsewhere$

If a random test was done on 2 students then, probability that they were both Covid-19 positive is given as,

$p(X=2)=\binom{8}{2}(3/8)^{2}*(5/8)^6=0.2346933$

The probability that both are Covid-19 negative is $1-0.2346933=0.7653067$.