A) Two cards are dealt off a well-shuffled deck. You win $1 if the two cards are of different suits. Find the probability of your winning?

b) A coin is tossed 5 times. What is the probability that the first toss is a head

or exactly 2 out of the five tosses are heads?

c) In a shuffled 52-card deck, what is the probability that neither the top nor

the bottom card is a heart?

d) A bag contains 20 red marbles, 20 green marbles and 20 blue marbles. You

reach in and grab 15 marbles. What is the probability that they are all the

same colour?

A.) 0.7647 b.) 13/ 16 C.) 0.9412 D.) 8.743 * 10^-10

Step-by-step explanation:

A)

Number of cards per suit = 13

Nunber of suits = 4

Probability = required outcome / Total possible outcomes

P(1) = probability of picking a card from a certain suit

P(1) = 13 / 52

Hence, probability that 2nd card will be from a suit different from the first :

Total possible outcomes = (52 - 1) = 51

Required outcomes = (13 * 3) = 39

= 39 / 51

= 0.7647

B.)

First toss being head :

Required outcome = H = 1

Total possible outcomes = T or H = 2

P(H) = 1/ 2

For 5 tosses

Total possible outcomes = 2^n = 2^5 = 32

Exactly 2 heads = 10

P(exactly 2 heads) = 10/32 = 5/16

1/2 + 5/16 = (8 + 5) / 16 = 13/16

c)

1 - P(both top and bottom are hearts)

Number of hearts = 13 ; number of cards = 52

P(both are hearts) = 13/52 * 12/51 = 0.05882

1 - 0.05882

= 0.94117

= 0.9412

d)

Either all marbles are red OR all marbles are green OR all marbles are blue

Total number of marbles = (20 + 20 + 20) = 60

Probability that all 15 marbles are of a certain color :

(20/60 * 19/59 * 18/58 * 17/57 * 16/56 * 15/55 * 14/54 * 13/53 * 12/52 * 11/51 * 10/50 * 9/49 * 8/48 * 7/47 * 6/46)

(2.9146E−10) + (2.9146E−10) + (2.9146E−10)

= 8.7438E−10

= 8.743 * 10^-10

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.