C If you randomly select three cards from a standard 52card

C. If you randomly select three cards from a standard 52-card deck, what is the probability that the first card will be a heart and the last two cards will be black?

D. You have a six-sided die. Four sides are painted blue and two sides are pained yellow. You roll the die three times. Compute the probability of each of the following sequences:

Blue, blue, blue

Yellow, yellow, yellow

Blue, yellow, blue

Blue, blue, yellow

Solution

In a standard 52 card deck----- there are 13 heart cards and 26 black cards.

probability that the first card is heart and last two cards are black =[(13C1)*(26C2)]/52C3 =13/68

Probabilty of the first sequence Blue blue blue= (4/6)^3 = 8/27

Probability of second sequence yellow yellow yellow =(2/6)^3 =1/27

probability of third sequence Blue yellow blue =(4/6)*(2/6)*(4/6) =4/27

Probability of fourth sequence Blue Blue yellow =(4/6)*(4/6)*(2/6) =4/27