Dependent or Independent
A) Are the following events independent or dependent?
You pick a card out from a standard deck and then flip a coin.
B) What is the probability of picking a red card and getting a heads?
A) Independent
B) 1/4
P(AandB)= P(A) * P(B)= 26/52 * 1/2=26/104=1/4
Two events that cannot happen simultaneously are...
mutually exclusive
A bowl contains four apples, three bananas, three oranges, and two pears. If one piece of fruit is selected at random, what is the probability of selecting an orange?
3/12=1/4
How many 10-letter patterns can be formed from the letters of the word BASKETBALL?
10!/(2!*2!*2!)=453,600
What are the odds of choosing a diamond from a standard deck of cards?
P(s)= 13/52=1/4
The arrangement of objects in a certain order is called a
Permutation
The probability of selecting a red marble, not replacing it, then selecting a green marble from a box of 6 red and 2 green marbles
A) Are these events dependent or independent?
B) Determine the probability
A) Dependent
B) 6/8 * 2/7 = 12/56=3/14
At a local high school, 34% of the students take a bus to school and 56% of the students walk to school. Find the probability of randomly selecting a student that takes a bus or walks to school and determine if these events are mutually exclusive or overlapping event?
34/100 + 56/100 = 90/100 or 90%
P(AorB)= P(A)+ P(B)
mutually exclusive
What is the probability of selecting a yellow or blue marble from a box of 5 green, 3 yellow, and 2 blue marbles?
P(yellow or blue)= P(yellow) + P(blue) = 5/10=1/2
Eight children are riding on a merry-go-round. How many ways can they be seated?
8!= 5040
Two number cubes are tossed. What are the odds that they show a sum greater than 9?
6/36=1/6 (5,5)(4,6)(6,4)(5,6)(6,5)(6,6)
the set of all possible outcomes of an event is called
sample space or tree diagram
You pick a card out of a deck, put it back, then pick another card
Are these events independent or dependent?
Independent
A card is drawn from a standard deck of cards. What is the probability of drawing a Jack or a Heart?
A) Are these events mutually exclusive or overlapping?
B) Determine the probability of the event
A) Overlapping event
B) 4/52 + 13/52 - 1/52 =16/52= 4/13
What is the probability of rolling two dice and getting a sum greater than 10
(5,6), (6,5), or (6,6)
3/36= 1/12
Find the number of possible arrangements of 9 different videos in a display window using exactly 4 at a time
P(9,4) = 3024
What is the probability of tossing 3 heads when three coins are tossed?
1/2*1/2*1/2=1/8
Events that can not happen at the same time are
mutually exclusive
You flip a coin and then flip the same coin again.
A) Are these events independent or dependent?
B) Find the probability of getting two heads
A) Independent
B) 1/2 * 1/2= 1/4
On a school board, 2 of the 4 female members are over 40 years of age, and 5 of the 6 male members are over 40. If one person did not attend the meeting, what is the probability that the person was a male or a member over 40?
4/5
P(male or over 40)= P(male) + P(over 40) - P(male and over 40) = 6/10+ 7/10 - 5/10= 8/10= 4/5
A bag contains 3 black, 5 green, and 4 yellow marbles.
What is the probability that 2 marbles selected a random will both be black?
P(2 black marbles)= 3/12*2/11=6/132= 1/22
The Environmental Club consists of 20 members, of which 9 are male and 11 are female. Seven members will be selected to form an event-planning committee. How many committees of 4 females and 3 males can be formed?
C(9,3)*C(11,4)= 27,720 possible committees
If two marbles are selected at random from a bag containing 6 red and 4 blue marbles, find the odds that both marbles are red.
P(both red)= 6/10*5/9=30/90= 1/3
What is an overlapping event?
An overlapping event is where an event has something in common that you need to subtract.
The probability of randomly selecting two dimes from a bag containing 10 dimes and 8 pennies if the first selection is replaced
A) Are these events independent or dependent?
B) Determine the probability of selecting two dimes
A) Independent
B) 10/18 * 10/18 =100/324= 25/81
The probability of selecting a card from a standard deck of cards and the card is a 10 or an ace
A) Determine if the event is mutually exclusive or overlapping and
B)Determine the probability
A) Mutually exclusive
B) 4/52 + 4/52= 8/52 = 2/13
Find the probability of randomly selecting 3 red pencils from a box containing 5 red, 3 blue, and 4 green pencils
5/12*4/11*3/10=60/1320=1/22
A company needs to choose an 8 person board of directors. If 24 different people applied, how many possible groups can there be?
Because order is not important (no specific roles)
C(24, 8)= 735,471
Two dice are tossed. What are the odds of getting a sum of 7 when two number cubes are tossed?
6/36=1/6 (3,4)(4,3)(2,5)(5,2)(1,6)(6,1)
How do you find the expected value of an event?
Expected value= P(event A)Value(Event A)+ P(Event B)Value(Event B)+....
There are two traffic lights along the route that Ms. Bella drives from home to work. One traffic light is red 50% of the time. The next traffic light is red 60% of the time. The lights operate on separate timers. Find the probability that these lights will both be red on Ms. Bella's way home from work.
A) Are these events independent or dependent?
B) Determine the probability that both lights will be red
A) Independent
B) 50/100 * 60/100 = 3/10 or 30%
A card is selected from a standard deck of cards. What is the probability of selecting an Ace or a black card?
A) Are these events mutually exclusive or overlapping?
B) Determine the probability
A) Overlapping event
B) 4/52 + 26/52 - 2/52 = 28/52 = 7/13
A survey of the junior class at SPF high school shows that 2/5 of the students who have home computers use them for word processing, 1/3 use them for playing games, and 1/4 use them for both word processing and playing games. What is the probability that a student with a home computer uses it for word processing or playing games?
29/60
P(AorB)= P(A) + P(B) - P(AandB)
P(AorB)= 2/5 + 1/3 - 1/4
= 24/60 + 20/60 - 15/60=29/60
How many ways can 10 people be seated around a circular conference table if there is a laptop computer on the table in front of one of the seats?
Has a fixed point (reference point) seat with laptop so
P(10,10)= 10!=3,628,800
You pull out one card from a standard 52 card deck. What is the probability of picking a red card or a three?
26/52+4/52-2/52=28/52=7/13
This is where order is not important
Combination
Jack had 4 Snicker bars and 8 Mars bars. He randomly chose a piece of candy, ate it, then chose another.
A) Are these events Dependent or Independent?
B) What is the probability that both candy bars were snickers?
A) dependent
B) 4/12 * 3/11=12/132= 1/11
On a spinner labeled with numbers 1-10, where each number is equally likely to be spun, determine the probability of spinning an odd number or a multiple of 3
P(odd) = 5/10
P(multiple of 3) = 3/10
P(odd and multiple of 3)= 2/10
5/10 + 3/10 - 2/10 = 6/10 = 3/5
The probability of two independent events occurring is 1/18. If the probability of one event is 1/3, find the probability of the other event
1/6
P(AandB)= P(A) * P(B)
1/18= 1/3 * x
x= 3/18 or 1/6
How many different arrangements can be made with ten pieces of silverware laid in a row if three are identical spoons, four are identical forks, and three are identical knives?
10!/(3!4!3!)=4200 different arrangements
Ms. E was planning a trip to the beach on Saturday but the weather forecast states that the chance of rain on Saturday is 65%. What is the probability that it won't rain on Saturday?
P(no rain)= 35/100
What is the formula for conditional probability?
P(B|A)=P(A and B)/P(A)