Question

a recent survey of technology professionals who work in silicon valley revealed that 63% have a masters degree. two technology professionals who work in silicon valley are randomly selected. assuming that the academic background of the professionals in silicon valley is independent of one another: (enter your answers below without rounding them)
a) what is the probability that both have a masters degree?
b) what is the probability that at least one of them has a masters degree?
c) what is the probability that neither one has a masters degree?

Explanation:

Step1: Define probabilities

Let \(P(A) = 0.63\) (probability of one having a master's degree). Then \(P(\text{not }A)=1 - 0.63=0.37\)

Step2: Solve part (a)

Since events are independent, \(P(\text{both})=P(A)\times P(A)\)
\(P(\text{both})=0.63\times0.63 = 0.3969\)

Step3: Solve part (c)

\(P(\text{neither})=P(\text{not }A)\times P(\text{not }A)\)
\(P(\text{neither})=0.37\times0.37=0.1369\)

Step4: Solve part (b)

Use the formula \(P(\text{at least one}) = 1 - P(\text{neither})\)
\(P(\text{at least one})=1 - 0.1369 = 0.8631\)

Answer:

a) \(0.3969\)
b) \(0.8631\)
c) \(0.1369\)