Question

Cards are drawn from a standard 52-card deck until the third club is drawn. After each card is drawn, it is put back in the deck and the cards are reshuffled so that each card drawn is independent of all others. (a) Find the probability that the 3rd club is drawn on the 8th selection. (b) Find the probability that at least 8 cards are drawn before the 3rd club appears. (c) Repeat parts (a) and (b) if the cards are drawn without replacement. That is, after each card is drawn, the card is set aside and not replaced in the deck.

Answer 1

Answer:

Step-by-step explanation:

Given that cards are drawn from a standard 52-card deck until the third club is drawn.

With replacement:

Drawing 3 club prob = 1/52 and non club = 51/52

a) Hence Prob (3rd club is drawn on the 8th selection)

= P(7 non 3 clubs, and one 3 club)

= $(\frac{51}{52} )^7 (\frac{1}{52})$

b) P(first 7 cards  non 3 club) = $(\frac{51}{52} )^7$

With replacement

c) P(7 non 3 clubs and 8th 3club)

= $\frac{51C7 }{52C8}$

d) P(atleast first 7 cards non3 club) =1-P(3 club in the 7th draws )=$1-\frac{51C7 }{52(52C8)}$