1.)

A card is randomly drawn from a standard -card deck. An ace of hearts wins the grand prize; any other ace or heart wins a small prize. What is the probability of winning a small prize? Express your answer as a common fraction. Assume that a grand prize winner does NOT also win a small prize.

2.)

The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the resulting number is divisible by 4? Express your answer as a common fraction.

3.)

Mario, Yoshi, and Toadette play a game of "nonconformity": They each choose rock, paper, or scissors. If two of the three people choose the same symbol, and the third person chooses a different symbol, then the one who chose the different symbol wins. Otherwise, no one wins.

If they play 4 rounds of this game, all choosing their symbols at random, what's the probability that nobody wins any of the 4 games? Express your answer as a common fraction.

4.)

A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability of selecting a blue marble from the bowl is 2/5. There are fewer than 100 marbles in the bowl. What is the probability of selecting a green marble and then a red marble from the bowl on the first two selections, assuming marbles are not returned to the bowl after being pulled?

Express your answer as a common fraction.

5.)

What is the probability that a randomly selected three-digit number has the property that one digit is equal to the product of the other two? Express your answer as a common fraction.

Jdaye
Feb 4, 2018

#1**+1 **

1.) There are 3 other aces and 12 more hearts that will win the small prize

And there are 52 possibilities when we draw a card from the deck.....

So....the probability of winning a small prize =

Favorable outcomes / Total possible outcomes =

[ 12 + 3 ] / 52 =

15 / 52

CPhill
Feb 4, 2018

#2**+1 **

4.)

A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability of selecting a blue marble from the bowl is 2/5. There are fewer than 100 marbles in the bowl. What is the probability of selecting a green marble and then a red marble from the bowl on the first two selections, assuming marbles are not returned to the bowl after being pulled?

There must be 65 marbles in the bowl because 5 and 13 have the lowest common multple of 65....

3/13 = 15/65 and 2/5 = 26/65

So

15 are red, 26 are blue and 65 - 15 - 26 = 24 are green

So...the probability of selecting green and then red =

(24/65) (15/64) = (24/64) (15/65) = ( 3/8) (3/13) = 9 / 104

CPhill
Feb 4, 2018

#3**+1 **

2). Of the 5 numbers given[2, 3, 4, 7, 8], we have the following pairs of numbers that each permutation of the 5 numbers must end in order to be divisible by 4. And they are as follows:

24, 28, 32, 48, 72, 84, or 6 pairs. Each of these pairs will cycle through all the permutations of the remaining 3 numbers, or 3!.

Therefore the probability that the resulting number is divisible by 4 will be:

**[6 x 3!] / 5! = 36 / 120 =30%.**

Guest Feb 4, 2018

edited by
Guest
Feb 4, 2018

#4**+1 **

5.)

What is the probability that a randomly selected three-digit number has the property that one digit is equal to the product of the other two? Express your answer as a common fraction.

To make Possible products # of Numbers

0 2nd, 3rd digits 0..1st digit 1 - 9 9

1 11 1

2 21 3

3 31 3

4 14 , 22 6

5 15 3

6 16 23 9

7 71 3

8 81 42 9

9 91 33 6

Prob = 52 / 900 = 13 / 225

CPhill
Feb 4, 2018