Question

about 5% 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? assume the events are independent.
the probability that both are left - handed is 0.0025
(round to four decimal places as needed)
the probability that at least one person is right - handed is
(round to four decimal places as needed)

Explanation:

Step1: Find the probability of the complement event

The complement of the event “at least one person is right - handed” is the event “both are left - handed”.
Let \(P(L)\) be the probability that a person is left - handed. Given \(P(L)=0.05\).
We know that for independent events \(A\) and \(B\), \(P(A\cap B)=P(A)\times P(B)\). The probability that both are left - handed is \(P(L_1\cap L_2)=0.05\times0.05 = 0.0025\) (where \(L_1\) is the event that the first person is left - handed and \(L_2\) is the event that the second person is left - handed)

Step2: Use the formula for the probability of the complement

Let \(A\) be the event “at least one person is right - handed”. Let \(B\) be the event “both are left - handed”.
We know that \(P(A)=1 - P(B)\)
Since \(P(B) = 0.0025\), then \(P(A)=1-0.0025\)

Answer:

\(0.9975\)