If the three cards are to be drawn and without any replacement from the deck of cards. Determine the probability that the event B1 ∩ B2 ∩ B3 wherein B1 is the events that the card is red ace, B2 is the 10 or jack, and B3 is greater that 3 but less than 7

Solution:

First, it is important to determine the events

            B1 : the card is red ace

            B2 : The card is 10 or jack

            B3 : the card is greater than 3 but it is less than 7

Then,

            P(B1) = 2/52

            P(B2/A1) = 8/51

            P (B3/ B1 ∩ B2) = 12/50

To get the probability of

P (B1 ∩ B2 ∩ B3) = P (B1)P(B2/B1) P(B3/(B1 ∩ B2)

                             = (2/52)(8/51)(12/50)

                             = 8/5525

 

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