A box contains two cards marked with a “0” and two cards marked with a “1.” Two cards will be sampled without replacement from this population.
a. What is the probability of drawing a “1” on the second draw given that the first draw is a “0”?
b. What is the probability of drawing a “1” on the second draw given that the first draw is a “1”?
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Before any cards are taken there is a 2:4; that is, 1:2 chance of picking either 0 or 1.
As one card is taken - a 0- the probability changes : only one card is a 0 and two cards are a 1 so the ratio changes to a 1:3 chance as the first card was retained.
Similarly for the other card. You can deduce the answer in the same manner: There are 3 cards left and only one of them is a 1. Therefore the chance is also 1:3
1:3 is the probability of taking a 0 from the pack on the second draw in the event a 0 was selected in the first draw and not returned and similarly for the number 1 under the same conditions - removing a 1 in the first draw.
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