Can you randomly draw two cards from a standard deck suppose you want to draw a queen twice in a row what is the probability of picking a queen on the second draw if the events are dependent
When the events are dependent, the probability of picking a queen on the second draw is dependent on whether a queen was picked on the first draw.
If a queen was picked on the first draw, then there are now only 3 queens left in the deck out of 51 total cards remaining. Therefore, the probability of picking a queen on the second draw given that a queen was picked on the first draw is 3/51.
If a queen was not picked on the first draw, then there are still 4 queens left in the deck out of 51 total cards remaining. Therefore, the probability of picking a queen on the second draw given that a queen was not picked on the first draw is 4/51.
Overall, the probability of picking a queen on the second draw when the events are dependent is given by the following formula:
P(queen on second draw) = P(queen on first draw) * P(queen on second draw | queen on first draw) + P(no queen on first draw) * P(queen on second draw | no queen on first draw)
= (4/52) * (3/51) + (48/52) * (4/51)
= (1/13) * (1/17) + (12/13) * (4/51)
= 4/221 + 48/663
= 12/221 + 48/663
= 60/221
≈ 0.2715
Therefore, the probability of picking a queen on the second draw when the events are dependent is approximately 0.2715, or about 27.15%.