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
(round to four decimal places as needed.)

Explanation:

Step1: Convert percentage to decimal

Given that \(5\% = 0.05\) (probability of one person being left - handed).

Step2: Use the multiplication rule for independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event that the first person is left - handed and \(B\) be the event that the second person is left - handed. Then \(P(A) = P(B)=0.05\). So \(P(A\cap B)=0.05\times0.05\).

Answer:

\(0.0025\)