Question

A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card. Let X be the number of cards you turn over until you observe the first red card. The probability that X is greater than 2 is:___________

Answer 1

Answer:

2/9

Step-by-step explanation:

given that a set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly and you turn cards over, one at a time, beginning with the top card.

Let X be the number of cards you turn over until you observe the first red card.

X can take values as 1,2,3,4,5 or 6.

No other possibility because at the worst 6th card has to be red

P(X>2) = 1-(P(X=1)+P(x=2))

P(X=1) = Prob for I card to be red = $\frac{1}{2}$

P(x=2) Prob for I card black and second red = $\frac{5*5}{10*9} =\frac{5}{18}$

$P(X>2) = 1-(\frac{1}{2} +\frac{5}{18} )\\= \frac{2}{9}$