I was able to do a and b. I\'m not sure how to go about part c. I saw some one a

Question

I was able to do a and b. I'm not sure how to go about part c. I saw some one answered this question but there was no explanation.

Consider a standard deck of cards, from which a person is dealt 5 cards.
a. What is the probability a person is dealt 3 diamonds and 2 clubs?
b. What is the probability a person is dealt 3 hearts?
c. Now the rules of the game have changed. Instead of being dealt the selected card, the player records the card on a piece of paper, after which, the card is returned to the deck. This is repeated 5 times. Repeat a. and b. above per the new rules.

Explanation / Answer

(a) Binomial Distribution

Number of possiblities of 3 diamonds out of 13 diamonds = 13C3 = 286

Number of 2 clubs out of 13 clubs = 2C13 = 78

So, number of possibilities of 3 diamonds and 2 clubs = 286 X 78 = 22308

Number of possibilities of 5 cards out of 52 cards = 2598960

So, Probability a person is dealt 3 diamonds and 2 clubs = 22308/2598960 = 0.0086

(b) Number of possibilities of 3 hearts out of 13 hearts = 3C13 = 286

Number of possibilities of 3 cards out of 52 cards = 3C52 = 22100

So, probability of a person is dealt with 3 heatrs = 286/22100 = 0.0129

(c) When the card is replaced after each trial:

P(diamond) = pD = 1/13 = 0.0769

P(club) = pc = 1/13 = 0.0769

Probability of 1st trial: diamond, 2nd trial: diamond, 3rd trial: diamond, 4th trial: club, 5th trail: club = pD3 pC2 = (0.0769)3 (0.0769)2 = 0.000002689

pH= 1/13 = 0.0769

Probabiliy of 1st trial: heart , 2nd trail: heart, 3rd trial: heart = pH3 = (0.0769)3 = 0.0004548

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