Probability of Technology Professionals Having a Master's Degree in Silicon Valley

Recent Survey Results

A recent survey of technology professionals who work in Silicon Valley revealed that 34% have a master's 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.

Probability Calculations

a) What is the probability that both have a master's degree?

b) What is the probability that at least one of them has a master's degree?

c) What is the probability that neither one has a master's degree?

Final Answer

The probability that both technology professionals have a master's degree is 0.1156. The probability that at least one of them has a master's degree is 0.4484. The probability that neither one has a master's degree is 0.4224.

Explanation

To calculate the probability that both technology professionals have a master's degree, we need to multiply the probability of the first professional having a master's degree by the probability of the second professional having a master's degree. Since the academic background of the professionals is assumed to be independent, the probability of each professional having a master's degree is 34%.

Therefore, the probability that both professionals have a master's degree is:

P(both have a master's degree) = P(first professional has a master's degree) * P(second professional has a master's degree)

P(both have a master's degree) = 0.34 * 0.34 = 0.1156

To calculate the probability that at least one of the professionals has a master's degree, we can subtract the probability that neither of them has a master's degree from 1. The probability that neither professional has a master's degree is the complement of the probability that at least one of them has a master's degree.

Therefore, the probability that at least one of the professionals has a master's degree is:

P(at least one has a master's degree) = 1 - P(neither has a master's degree)

P(at least one has a master's degree) = 1 - (1 - 0.34) * (1 - 0.34) = 0.4484

Finally, to calculate the probability that neither professional has a master's degree, we can multiply the probability of the first professional not having a master's degree by the probability of the second professional not having a master's degree.

Therefore, the probability that neither professional has a master's degree is:

P(neither has a master's degree) = P(first professional does not have a master's degree) * P(second professional does not have a master's degree)

P(neither has a master's degree) = (1 - 0.34) * (1 - 0.34) = 0.4224

What is the probability that both have a master's degree?

What is the probability that at least one of them has a master's degree?

What is the probability that neither one has a master's degree?

The probability that both technology professionals have a master's degree is 0.1156. The probability that at least one of them has a master's degree is 0.4484. The probability that neither one has a master's degree is 0.4224.

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