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According to an​ article, 43​% of adults have experienced a breakup at least once during the...

According to an​ article, 43​% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected​ adults, find the probability that the​ number, X, who have experienced a breakup at least once during the last 10 years is

a. exactly​ five; at most​ five; at least five.

b. at least​ one; at most one.

c. between three and five​, inclusive.

d. Determine the probability distribution of the random variable X.

Math   Statistics-And-Probability   
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Answer #1

Here, in this example we observed that the random variable x is the number of adults have experienced a breakup at least once during the last 10 years.

p = probability of success that is the adults have experienced a breakup at least once during the last 10 years = 43%=0.43

we are select 9 adults randomly i.e.n=9

Since x is dichotomous random variable and p is probability of adults experienced a breakup at least once during the last 10 year remain constant . Therefore x follow the Binomial Distribution with n=9 and p= 0.43.

The probability mass function of random variable x is:

P( X = x) =n​​​​​​C​​​​​x​ p​​​​​​​​​​​x q(n-x).    ,X=0,1,2,...9 , p+q= 1

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