+54 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.
+129899 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
+129899 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
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%.
+129899 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
