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In an introductory statistics class, the number of males and females are shown in the following frequency distribution table: Sex Frequency Male 17 Female 23 Two students are selected at random without replacement from the class. Find the probability that the first student selected is female and second is male?
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In an introductory statistics class, the number of males and females a...
Calculating the Probability of Selecting a Female and then a Male
To calculate the probability of selecting a female first and then a male, we need to consider the total number of males and females in the class.

Step 1: Calculate the Probability of Selecting a Female First
- Total number of females = 23
- Total number of students in the class = 17 (males) + 23 (females) = 40
Therefore, the probability of selecting a female first is:
P(Female) = Number of females / Total number of students = 23 / 40 = 0.575

Step 2: Calculate the Probability of Selecting a Male Second
- After selecting a female, there are 22 females left and 17 males left in the class
Therefore, the probability of selecting a male second, given that a female was selected first, is:
P(Male | Female) = Number of males / Total number of students remaining = 17 / 39 = 0.435

Step 3: Calculate the Overall Probability
To find the overall probability of selecting a female first and then a male, we multiply the probabilities from Step 1 and Step 2:
P(Female and then Male) = P(Female) * P(Male | Female) = 0.575 * 0.435 = 0.250125
Therefore, the probability that the first student selected is female and the second student selected is male is 0.250125 or approximately 25.01%.
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In an introductory statistics class, the number of males and females are shown in the following frequency distribution table: Sex Frequency Male 17 Female 23 Two students are selected at random without replacement from the class. Find the probability that the first student selected is female and second is male?
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