My problem is in understanding the wording: Given a group of boys and girls- 2 students are selected at random one after another, without replacement. Do the statements: "probability that 1st student is male and 2nd student is female" mean the same as "probability of selecting a female student given that 1st is male." Would the implications be any different if the same selection was done with replacement?
2026-04-25 18:17:13.1777141033
Conditional Probability wording of question
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No, in general $P(B \mid A)$ (probability of $B$ given $A$) is not the same thing as $P(A \cap B)$ (probability of $A$ and $B$).
The answers to various probability questions will change, depending on whether you select students with or without replacement. But you cannot treat $P(B \mid A)$ and $P(A \cap B)$ as if they were the same thing in either case.