Probability and Counting

A jar contains 3 red marbles, 9 green marbles, and 5 blue marbles. What is the probability that you draw 4 green marbles in a row if you do replace the marbles after each draw?

.0785550949

Suppose A and B are events in a sample space with P(A)=0.69,P(B)=0.65,P(B∪A)=0.83 P(A∩B)

.51

P(B|A)

.73913043

P(A|B)

.78461538

If we draw 7 cards from a standard 52 card deck, what is the probability that all 7 cards are hearts?

0.00001282659

A family has 4 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 4 girls if it is known the family has at least one girl.

1/15

3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 9

1/27

If two dice are rolled, find the probability that the sum of the die is 7.

1/6

License plates in Florida have the form A24BSDE; that is, a letter followed by 2 digits followed by 4 more letters. Number of possible license plates

1188137600

Three students from a 21 student class will be selected to attend a meeting. 6 of the students are female.

120/7980

A diagnostic test for disease X correctly identifies the disease 94% of the time. False positives occur 12%. It is estimated that 3.71% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.) The percentage chance that the test will be positive The probability that, given a positive result, the person has disease X

15.0422 23.18410871

3 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 13 freshmen and 12 sophomores, in how many different ways can the conference attendees be selected?

18876

A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4, 5 and 6 are replaced by 1, 2 and 3 respectively. 3 three-dice (with sides labeled 1, 2, and 3) are rolled and the numbers face up on the 3 dice are recorded. Give the sample space for this experiment. What is the probability that at least one of the dice rolled is showing a 2?

19/27

A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4, 5 and 6 are replaced by 1, 2 and 3 respectively. 3 three-dice (with sides labeled 1, 2, and 3) are rolled and the numbers face up on the 3 dice are recorded. Give the sample space for this experiment. What is the probability that at least one of the dice rolled is showing a 3?

19/27

What is the probability that you draw 4 green marbles in a row if you do not replace the marbles after each draw?

21/646

Griff would like a plate that ends in MWSU. How many such plates are there? Number of possible license plates

2600

A jar contains 4 red marbles, 9 green marbles, and 6 blue marbles. What is the probability that you draw a red marble?

4/19

Two dice are rolled and someone indicates that the two numbers that come up are different. Find the probability that the sum of the two numbers is 6.

4/30

In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.

45/7084

2. Both marbles drawn are red

5/26

Faculty at a certain university need to create a committee to evaluate the general studies curriculum offered on campus. If there are 29 faculty members and they must select a chair, vice chair, secretary and 6 additional faculty members to be on the committee, in how many ways can the committee be formed?

5047562520

Steve interviewed several musicians to be a part of his band. If he interviewed 3 guitarists, 3 drummers, and 6 vocalists, and the band consists of one guitarist, one drummer, and one vocalist, how many different bands can Steve create?

54

An ice cream shop has 20 flavors. You also have the choice of a sugar cone, waffle cone or cup. If a person orders two scoops of different flavor ice cream, how many possible orders are there, if you do not care about the order of flavors?

570

Three students from a 20 student class will be selected to attend a meeting. 11 of the students are female.

5850/6840

An ice cream shop has 21 flavors. You also have the choice of a sugar cone, waffle cone or cup. If a person orders a one scoop ice cream, how many possible orders are there?

63

The math club wants to choose a committee to plan the back to school party. How many 3 person committees can be formed from the set of 17 members?

680

A bag contains 6 red marbles and 7 white marbles. Two marbles are drawn in succession without replacement. Find the probabilities of the following events: 1. The first marble drawn is red and the second is white.

7/26

3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?

7/27

What is the probability that you choose exactly one of each color, if you pick 3 from the jar?=

72/323

The math club needs to select a President, Vice President, Treasurer and Secretary from their 32 members. How many ways can they do this?

863040

A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns are possible if the first 3 digits must be even and the last digit cannot be zero, one or two?

8750

A jar contains 2 red, 3 green, 7 blue, and 3 yellow marbles. If a single marble is chosen at random from the jar and its color recorded, give the sample space. What is the probability of each possible outcome?

R=2/15 G=3/15 B=7/15 Y= 3/15