Mutually Exclusive or Overlapping events
FREEEEEE
you know, if you don't think you can solve anything else
*regrets life decisions*
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
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)
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?
(for 50 extra points)
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
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
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
(for 50 extra points)
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)
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?
(for 50 extra points)
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
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