+0  
 
+1
671
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avatar+33 

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
avatar+89909 
+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

 

 

cool cool cool

CPhill  Feb 4, 2018
 #2
avatar+89909 
+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

 

 

cool cool cool

CPhill  Feb 4, 2018
 #3
avatar
+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
avatar+89909 
+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

 

 

cool cool cool                        

CPhill  Feb 4, 2018

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