Dependent/Independent &
Overlapping/Mutually Exclusive
Overlapping/Mutually Exclusive
Probability
Permutations and Combinations
100
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
100
What are the odds in favor of choosing a diamond from a standard deck of cards?
P(diamond)= 13/52
Odds in favor = 13/39
100
This is where order is not important
Combination
200
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
200
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
200
The arrangement of objects in a certain order is called a
Permutation
300
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
300
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
300
Eight children are riding on a merry-go-round. How many ways can they be seated?
8!= 40320
400
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
400
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 are the odds against it raining on Saturday?
P(no rain)= 35/100
Odds against it raining = 35/65
400
A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the middle and a camper who has a tendency to engage in food fights must sit to the counselor's immediate right?
3 x 2x 1 x 1 x 1 = 6
500
The probability of randomly selecting two dimes from a bag containing 10 dimes and 8 pennies if the first selection is not replaced
A) Are these events independent or dependent?
B) Determine the probability of selecting two dimes
A) Dependent
B) 10/18 * 9/17 =90/306= 5/17
500
Find the probability of randomly selecting 3 red pencils from a box (without replacement) containing 5 red, 3 blue, and 4 green pencils
5/12*4/11*3/10=60/1320=1/22
500
Find the number of possible arrangements of 9 different videos in a display window, placed in order, using exactly 4 at a time
P(9,4) = 3024
600
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? Are these events mutually exclusive or overlapping?
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
Overlapping
600
A construction company is planning to bid on a building contract. The bid costs the company $1200. The probability that the bid is accepted is 1/10. If the bid is accepted, the company will make $62,000 minus the cost of the bid.
What is the expected value in this situation?
E = P(accept) x A(accept) + P(reject) x A (reject)
E = 1/10 x 60800 + 9/10 x -1200
E = $5000
600
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
700
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
700
The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting an odd number, given that a blue disk is selected.
(P( odd and blue))/(P(blue))
(3/8)/(5/8)
= 3/5
700
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