13. Southpaws About 13% of the population is left-handed. Iftwo people are randomly selected, what is the probability thatboth are left-handed? What is the probability that at least one isright-handed?

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Step 1

Identifying the distribution:

Consider the event X that a people having left hand as a “success”.

There are 2 people. Each question can be considered as a trial. So, there are n = 2 trials.

Now, the people are randomly selected. Moreover, one people is independent of another. So, the 2 trials are independent of one another.

Here, the probability of getting a “Success” is 0.13.

The probability of a success is p = 0.13, which is constant for all trials.

Consider X as the number of successes (number of people having left-handed) out of the n = 2 trials.

Thus, X has a Binomial distribution with parameters n = 2 and p = 0.13. Since X is a discrete random variable, X has a Binomial pmf (probability mass function).

Step 2

The required probability is P (Both are left-handed). The required probability is obtained as shown below:

Step 3

Thus, the probability P (Both are ...

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