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?
0.3969
b) what is the probability that at least one of them has a masters degree?
0.8631
c) what is the probability that neither one has a masters degree?
0.1369

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: Calculate probability for part (a)

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

Step3: Calculate probability for part (b)

Use the complement rule. \( P(\text{at least one}) = 1 - P(\text{neither}) \)
First find \( P(\text{neither})=P(\text{not }A)\times P(\text{not }A)=0.37\times0.37 = 0.1369 \)
Then \( P(\text{at least one})=1 - 0.1369=0.8631 \)

Step4: Calculate probability for part (c)

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

Answer:

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