Questions: A recent study of 200 nurses found that of 125 female nurses, 56 had bachelor's degrees; and of 75 male nurses, 34 had bachelor's degrees. If a nurse is selected at random, find the probability that the nurse is a) a female nurse with a bachelor's degree b) a male nurse c) a male nurse with a bachelor's degree d) based on your answer to a, b, and c, explain which is most likely to occur. Why?

Solution Steps

The total number of nurses is 200. The number of female nurses with bachelor's degrees is 56. The probability \( P(a) \) is calculated as: \[ P(a) = \frac{\text{Number of female nurses with bachelor's degrees}}{\text{Total number of nurses}} = \frac{56}{200} = 0.2800 \]

The number of male nurses is 75. The probability \( P(b) \) is calculated as: \[ P(b) = \frac{\text{Number of male nurses}}{\text{Total number of nurses}} = \frac{75}{200} = 0.3750 \]

The number of male nurses with bachelor's degrees is 34. The probability \( P(c) \) is calculated as: \[ P(c) = \frac{\text{Number of male nurses with bachelor's degrees}}{\text{Total number of nurses}} = \frac{34}{200} = 0.1700 \]

Final Answer