Question 1206926: 3 Cards are drawn in succession without replacement from an ordinary deck. Find the probability of the event A1 ∩ A2 ∩ A3, where A1 is the event that the first card is RED ace, A2 is the event that the second card 10 or a jack and A3 is the event that the third card which is greater than 3 and less than 7?
Answer by math_tutor2020(3817)   (Show Source):
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Answer: 8/5525
Work Shown
A1 = first card is red ace
A2 = second card is 10 or jack
A3 = third card is between 3 and 7, excluding both endpoints
P(A1) = 2/52 = 1/26
This is because there are 2 red aces (hearts and diamonds) out of 52 cards total.
P(A2 given A1) = 8/51
This is because there are 8 cards that are either labeled "10" or "jack", out of 51 remaining cards.
P(A3 given A1 and A2) = 12/50 = 6/25
Note there are 12 cards labeled either "4", "5", or "6" and there are 50 cards remaining.
Multiply out those fractions: (1/26)*(8/51)*(6/25) = 48/33150 = 8/5525
8/5525 = 0.001447963800905 approximately
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