Suppose that I have a regular deck of 52 playing cards a If

Suppose that I have a regular deck of 52 playing cards.
(a) If I choose a single card at random, what is the probability that it will be a queen of spades?
(b) If I keep the first card I drew in (a), and draw a second card at random, what is the probability that one of them will be the queen of spades?
(c) If I continue in this way, drawing cards without replacing them, how many cards do I need to draw before there is a probability of 90% (or more) that I will have drawn the queen of spades?

Solution

a)

we have 52 cards and just 1 is a queen of spades

so

P(queen of spades ) = 1/52 = 0.019 = 1.9%

b)

as you keep 1 card we have just 51 cards and its your second trial

so

P(queen of spades) = 1/51 = 0.0196 = 1.96%

c)

if you continue drawing cards without replacing them

you will need to have only 1 card for you can have a probability of 90% or more that you will have drawn the queen of spades

there is only 1 solution here because you only have 1 favorable cases that is 1 queen of spades

if you would have 2 cards the probability of drawn the queen of spades will be 1/2 = 0.50 = 50%

so the only solution is to have only 1 card that is the queen of spades