A poll was taken of 10,439 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below.

Education Level Male Female Total
High School or Less 2023 3264 5287
Bachelor's Degree 2225 2113 4338
Master's Degree 416 305 721
Ph.D. 45 48 93
Total 4709 5730 10,439

A person is selected at random. Compute the following probabilities.

What is the probability that the selected person does not have a Master's degree, given that he is male?

To find the probability that the selected person does not have a Master's degree, given that he is male, we need to calculate the conditional probability.

Conditional probability is calculated using the formula:
P(A|B) = P(A and B) / P(B)

In this case, we want to find the probability that the person does not have a Master's degree (A), given that he is male (B).

Step 1: Calculate P(A and B) - the probability that the person does not have a Master's degree and is male.
From the table, we see that the number of males without a Master's degree is 4709 - 416 = 4293.

P(A and B) = 4293 / 10,439

Step 2: Calculate P(B) - the probability that the person is male.
From the table, we see that the total number of males is 4709.

P(B) = 4709 / 10,439

Step 3: Calculate the conditional probability, P(A|B).
Using the formula above, we have:
P(A|B) = P(A and B) / P(B)
= (4293 / 10,439) / (4709 / 10,439)
= 4293 / 4709
≈ 0.91

Therefore, the probability that the selected person does not have a Master's degree, given that he is male, is approximately 0.91 or 91%.