Lol probability question,, help pleeease!?

Question

Hey people, I'm starting yr 11 of school nxt year and and I'm doing some maths revision in the hols cuz Im a good boy :-) ;). Please could you answer this question and show me how u worked it out, so I can learn for myself. Thanks every1!!

A card is drawn at random from a pack of 52 playing cards. The card is replaced and a second card is drawn. This card is replaced and a third card is drawn. What is the probability of drawing:

b)at least two hearts

c) exactly one heart

Answer 1

this question is not possible with those choices

Answer 2

P(at least 2 hearts)=P(2) + P(3) = 3C2 (1/4)^2 (3/4)^1  +

3C3 (1/4)^3 (3/4)^0  =  5/32

P(one heart) = 3C1 (1/4)^1 (3/4)^2 = 3 (1/4)(9/16) = 27/64

ANSWER

Answer 3

Each drawing is independent of the other drawings.

b) There are 3 different ways you can get 2 hearts and 1 way to get all three hearts.

H = Heart

N = Non-heart

Combinations are: HHH, HHN, HNH, or NHH.

The probability of drawing a heart is 13/52 or 1/4.

The probability of drawing a non-heart is 39/52 or 3/4.

Probability of HHH = 1/4 *1/4 * 1/4 = 1/64

Probability of HHN = 1/4 * 1/4 * 3/4 = 3/64

Probability of HNH = 1/4 * 3/4 * 1/4 = 3/64

Probability of NHH = 3/4 * 1/4 * 1/4 = 3/64

Probability of one of these events is 1/64 + 3/64 + 3/64 + 3/64 = 10/64 = 5/32

c) Ways to get one heart is HNN, NHN, and HHN

Probability of HNN = 1/4 * 3/4 * 3/4 = 9/64

Probability of NHN = 3/4 * 1/4 * 3/4 = 9/64

Probability of NNH = 3/4 * 3/4 * 1/4 = 9/64

Probability of one of these combos = 9/64 + 9/64 + 9/64 = 27/64

Answer 4

There are 13 hearts in a deck of 52.  So, if you want at least two hearts, the probability is:

13/52 * 13/52 * 52/52

8788/140608

13/208, or 0.0625

If you want exactly one heart, one of them is going to be 13, but the other two are going to be 39 because there are 39 not hearts in a deck of cards.

13/52 * 39/52 * 39/52

19773/140608

9/64, or 0.140625

Answer 5

I think answer A is 3/16.

1/4 chance per go.

Gettting two hearts=1/4*1/4=1/16

Three different combinations (1+2, 2+3, 1+3)=3/16

That's all I can do

Answer 6

n = 3 , times we drawn a Card

probability for picking a heart

p(heart) = 13/ 52 = 1/4

q = 1 - p = 3/4

p (exactly one heart) =

3nCr1 * p^1 * q^(n-r)

3 * 1/4 * (3/4)²   = 3*3*3 / (4*4*4) = 27/64

p( at least two hearts) = p(exactly 2 hearts) + p(exactly3 hearts) =

3* (1/4)² * 3/4 + 1* (1/4)³ = 9/64 + 1/64 = 10/64 = 5/32