Question
Asked Sep 23, 2019
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13. Southpaws About 13% of the population is left-handed. If
two people are randomly selected, what is the probability that
both are left-handed? What is the probability that at least one is
right-handed?
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13. Southpaws About 13% of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-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).

p" (1-р)", х -0.1....»:0 < p<1:q-1-р
n-x
f (x)
|0.
Here
otherwise
2
f (x)= x(0.13) (1-0.13)*, x=0,1.2
otherwise
[0.
That is
2
(0.13) (0.87).x0.1,2
f (x)
otherwise
|0,
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p" (1-р)", х -0.1....»:0 < p<1:q-1-р n-x f (x) |0. Here otherwise 2 f (x)= x(0.13) (1-0.13)*, x=0,1.2 otherwise [0. That is 2 (0.13) (0.87).x0.1,2 f (x) otherwise |0,

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Step 2

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

P(Both are left-handed)= P(x 2)
2
13' (0.87)
2
=0.0169
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P(Both are left-handed)= P(x 2) 2 13' (0.87) 2 =0.0169

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Step 3

Thus, the probability P (Both are ...

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Math

Statistics

Hypothesis Testing

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