Probability Review
A committee of 6 members is chosen from a group of 12 Republicans & 10 Democrats. What is the probability that there will be no more than 2 Democrats?
(12C4 / 22C6) + (12C5 / 22C6) + (12C6 / 22C6)
A box contains 4 red cubes & 7 white cubes. If 3 cubes are drawn, what is the probability that they are the same color?
(4C3 / 11C3) + (7C3 / 11C3) = 13/55
How many permutations can be made when the number formed from digits 1, 2, 1, & 3 must be a multiple of 3?
1 + 2 + 1 + 3 = 7; 7 isn't divisible by 3. Therefore, 0.
10 slips of paper numbered from 6 to 15 are placed in a hat. 1 slip of paper is drawn. What is the probability that the number on the slip drawn is prime?
1/10 * 3 = 3/10
What is the probability of getting a number less than 4 in a toss of die?
1/3 * 3 = 1/2
What is the probability of drawing a red 7 from a bridge deck?
1/52 * 2 = 1/26
What is the probability of getting a 2 or 5 in a toss of die?
1/6 * 2 = 1/3
What is the probability of getting a multiple of 3 in a toss of die?
1/6 * 2 = 1/3
How many lines are determined by 10 points, no 3 of which are on the same line?
10 - 1 = 9, 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45
10 members of a football team huddle in a circle around the quarterback to hear the next play. In how many ways can they arrange themselves?
10! / 10 = 362,880
How may ways can you choose a committee of 5 girls & 7 boys from a group of 10 girls & 11 boys? (Find the number of combinations for girls, then for boys. Then find the product.)
10C5 * 11C7 = 83,160
A committee of 6 members is chosen from a group of 12 Republicans & 10 Democrats. What is the probability that there will be no Republicans?
10C6 / 22C6 = 210/74,613
How many ways can 6 ice cream flavors be selected out of 11 flavors?
11C6 = 462
How many ways can 3 identical math books, 4 identical physics books, & 7 identical English books be placed on a shelf?
3 + 4 + 7 = 14, 14! / 3! 4! 7! = 120,120
How many ways can 5 boys be selected for a basketball team out of a physical education class of 30 boys?
30C5 = 142,509
How many permutations can be made when the number formed from digits 1, 2, 1, & 3 must be an even number?
4 - 1 = 3, 3! = 6
A card is drawn from a bridge deck of 52 cards. Then, without replacing the 1st card, a 2nd card is drawn. Find the probability that the 1st card is a queen & the 2nd card is a spade.
4/52 * 26/51 = 2/51
How many ways can you draw 2 cards from a deck of 52 cards?
52C2 = 1,326
How many ways can you draw 56 marbles from a bag that contains 59 marbles?
59C56 = 32,509
In how many ways can 6 people be lined up for a photograph if Ralph must stand immediately to the left of Bernice?
6 - 1 = 5, 5! = 120
How many permutations can be made from the digits in the numeral 121221?
6! / 3! 3! = 20
A bag contains 3 red cubes & 6 white cubes. What is the probability of choosing a cube that isn't red?
6/9 = 2/3
At the head table at a banquet are seated 2 senators, 2 governors, & 3 mayors. Find the number of ways in which these 7 people can be seated with a governor at each end.
7 - 2 = 5, 5! / 2! 3! = 10
Each of 7 cheerleaders stands in a line holding a pompom. There are 3 white pompoms, 2 blue ones, & the rest are yellow. In how many distinguishable ways can the pompoms be arranged?
7! / 3! 2! 2! = 210
How many ways can you choose a group of 4 or more from a group of 7?
7C4 + 7C5 + 7C6 + 7C7 = 64
How many permutations of the letter in the word REPLICA end in a vowel?
7P3 = 210
How many 4-digit integers can be formed from the digits 0, 1, 2, 3, 4, 5, & 6 when no digit is repeated in an integer?
7P4 = 840
How many permutations of 4 letters each can be formed from the letters of the word NUMBERS?
7P4 = 840
How many 4-digit integers can be formed from the digits 0, 1, 2, 3, 4, 5, & 6 when repetitions are allowed?
7^4 = 2,401
In how many ways can 6 out of 8 people be seated in 6 empty seats?
8P6 = 20,160
Find the number of batting orders for 9 baseball players when the best 2 batters must be in the second & third positions.
9 - 2 = 7, 7! * 2 = 10,080
Find the number of permutations that can be made from the letters of the word SATELLITE.
9! / 2! 2! 2! = 45,360
At a safety program, a traffic instructor wishes to display 9 traffic signs. In how many different ways can she display the signs in a row when there are 4 identical stop signs, 2 identical direction signs, & 3 identical speed limit signs?
9! / 4! 2! 3! = 1,260
In how many ways can 9 different books be arranged on a shelf?
9! = 362,880
Odds
Number of successes / number of failures
Probability
Number of successful outcomes / number of possible outcomes
What is the probability AND odds of drawing a 3 in a random selection of the numbers 1, 2, 3, 4, 5, 6, 7, & 8?
Probability = 1/8; odds = 1/7
What is the probability AND odds of drawing an even number in a random selection of the numbers 1, 2, 3, 4, 5, 6, 7, & 8?
Probability = 4/8 = 1/2; odds = 4/4 = 1
