Question

2. cards are drawn from a decko 32 cards without replacement. What is the probability of getting both
Cards black or getting ove card queen and the other king​

Answer 1

Answer:

Let Q1 be the event that we draw a queen on the first draw. Since there are 4 queens in a deck of cards the probability of drawing a queen is

Pr(Q1) = 4/52

Let Q2 be the event that we obtain a queen on the second draw. Then the event Q2|Q1 is the event that we draw a queen on the second draw proved that the first card drawn was a queen.

Now consider the probability of drawing a queen on the second draw GIVEN that a queen was drawn on the first draw is

PR(Q2|Q1) = 3/51 because there are only 3 queens left in the deck. Before we drew the second time there were only 51 cards left in the deck.

Note that the two events described above are not independent because Or(Q1) is not equal to Pr(Q2|Q1). There are dependent events. Hence, the joint probability Pr(Q1 and Q2) or P(Q1, Q2) is given by

Pr(Q1 and Q2) = Pr(Q1,Q2) = Pr(Q2|Q1)Pr(Q1)=(3/51)(4/52)

I leave the computations to the reader and his or her calculator.

If you instructor has introduced probability trees I would recommend that you use them to d love this problem.

Masseuse the notation as I answered this question from my kindle

Explanation: