Counting Techniques
Find the number of possibilities: Five rooms in a house need to be painted. Each room can be painted white, yellow, or pink.
243
1/6
Independent or Dependent and calculate: You flip a coin twice. The first flip is tails-up and the second is heads-up.
Independent, 1/4
Mutually Exclusive or Overlapping and calculate: You roll a fair six-sided die. The die shows an even number or a number greater than three.
P or C and calculate: Shreya has homework in six subjects. She is deciding what order to complete them in.
Permutation; 720
Evaluate: 14C6
3003
A bowl of goldfish has 12 females and 8 males. If you select a fish at random, what is the probability that it will be female?
3/5
Independent or Dependent and calculate: Your sock drawer has 6 white socks, 4 brown socks, and 6 black socks. You randomly pick two socks and get a matching pair of black socks.
Dependent; 1/8
Mutually Exclusive or Overlapping and calculate: A bag contains 4 white jerseys numbered 1-4 and three 3 jerseys numbered 1-3. You randomly pick a jersey. It is red or has a number greater than 2.
Overlapping, 5/7
Find the number of permutations of the letters in the word ROOMMATE
10080
Evaluate: 7P5
2520
A jar of pens has 6 black pens, 4 red pens, and 7 blue pens. If a pen is selected at random, what is the probability that it will be red?
4/17
Independent or Dependent and calculate: A cooler contains 11 bottles of sports drink: 5 lemon-lime and 6 orange. You randomly grab one and give it to your friend, then grab a bottle for yourself. You both get lemon-lime.
Dependent, 2/11
Mutually Exclusive or Overlapping and calculate: A bag has 5 red marbles, 3 blue marbles, and 3 yellow marbles. You randomly pick a marble. It is red or blue.
Mutually Exclusive, 8/11
40320
P or C and calculate: A group of 25 people are going to run a race. The top three runners earn gold, silver, and bronze medals.
Permutation, 13800
Stanford University received 16,842 applications for the 1997-1998 school year. Of these, 2596 were accepted. What is the probability that any random applicant was accepted?
1298/8421
Independent or Dependent and calculate: A bag contains 6 red marbles and 4 blue marbles. You randomly pick a marble then put it back. Then you pick another marble. Both are red.
Independent, 9/25
Mutually Exclusive or Overlapping and calculate: A box of chocolates contains four milk chocolates, four dark chocolates, and three white chocolates. You randomly select a chocolate. It is milk or dark chocolate.
Mutually Exclusive, 8/11
Independent or Dependent and calculate: You have 12 shirts: 7 blue and 5 green. You randomly pick one to wear on Monday and then another on Tuesday. You wear blue on Monday and green on Tuesday.
Dependent, 35/132
P or C and calculate: A team of 15 soccer players needs to choose two players to refill the water cooler.
Combination, 105
Two dice are rolled. What is the probability that the sum of the numbers on the dice will be 7?
1/6
Independent or Dependent and calculate: A basket has 4 apples and 7 peaches. You randomly pick a piece of fruit and then put it back. Then you pick another piece of fruit. The first is an apple and the second is a peach.
Independent, 28/121
Mutually Exclusive or Overlapping and calculate: A litter of kittens consists of 1 gray female, 3 gray males, 3 black females, and 1 black male. You randomly pick a kitten. It is black or female.
Overlapping, 5/8
Mutually Exclusive or Overlapping and calculate: A cooler has 12 bottles of sports drink: 3 lemon-lime, 4 orange, and 5 fruit punch. You randomly grab a bottle. It is lemon-lime or orange flavored.
Mutually Exclusive, 7/12