SOLUTION: 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

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Question 1206927: 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?

Found 2 solutions by greenestamps, math_tutor2020:
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


P(A1):
There are 52 cards, of which 2 are red aces -- probability 2/52

P(A2):
There are 51 cards left; 4+4=8 of them are either 10 or jack -- probability 8/51

P(A3):
There are 50 cards left; there are 4 each of 4, 5, and 6, for a total of 12 -- probability 12/50

P(A1 ∩ A2 ∩ A3) = P(A1)*P(A2)*P(A3) = (2/52)(8/51)(12/50)

Perform the arithmetic and express the result in the required form.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Refer to this link where I provided the solution.
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1206926.html

Tutor greenestamps has the right idea, but P(A2) should be P(A2 given A1) since the event A1 occurs first. And it will alter what happens with A2.

Similarly, P(A3) should be something along the lines of P(A3 given A1 and A2) or P(A3 given (A1 ∩ A2) ) to signal that events A1 and A2 occured before A3.