Four cards are drawn in succession with replacement from a s

Four cards are drawn in succession with replacement from

a standard deck. At each draw, all the remaining cards in the deck are

equally likely. What is the probability of the color sequence red-red-black-

red?

Solution

Four cards drawn with replacement.

Hence after every draw again prob is independent.

There are 26 black and 26 red cards for every draw.P(red) =0.5 P(Black) =0.5

For the colour sequence red- red black-red = (0.5)(0.5)(0.5)(0.5) = (0.5)4

= 0.0625