A bag contains 2 red checkers and 6 black checkers. A checker is selected, kept out of the bag, and then another checker is selected. What is P(black, then red)?

A bag contains 2 red checkers and 6 black checkers. A checker is selected, kept out of the bag, and then another checker is selected. What is P(black, then red)?

Answers (1)

There are 6 black checkers out of the 8 checkers so the probability of selecting a black checker on the first draw is:
P(black first)=\(\displaystyle\frac{{6}}{{8}}=\frac{{3}}{{4}}\)
Since the checker is not replaced, then there are now 7 checkers left so the probability of selecting a red checker on the second draw is:
P(red second)=\(\displaystyle\frac{{2}}{{7}}\)
So, the probability of drawing a black checker first, then a red checker second is:
P(black, the red)=\(\displaystyle{\left(\frac{{3}}{{4}}\right)}\cdot{\left(\frac{{2}}{{7}}\right)}\)
P(black, the red)=\(\displaystyle\frac{{6}}{{28}}\)
P(black, the red)=\(\displaystyle\frac{{3}}{{14}}\)

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