Hats only: 7
Jackets only: 9
Middle: 3
Outside: 1
Bob flips 2 fair coins. Repersent this in a tree diagram.
1/2: heads
1/2: heads
1/2: tails
1/2: tails
1/2: heads
1/2: tails
What is the conditional probability formula?
P(A|B)=P(A and B)/P(B)
Sample space is a list of possible outcomes.
p: It is Tuesday.
q: It is raining.
Write in words p V q.
It is Tuesday or it is raining.
Only work: 15
Only slacks: 5
Work and Slacks: 5
Outside: 5
A bag has 2 blue marbles and 5 green marbles. You draw 2 marbles from the bag with replacement. Represent this in a tree diagram.
2/7 blue
2/7 blue
5/7 green
5/7 green
2/7 blue
5/7 green
In a group of 40 boys, 23 have dark hair, 18 have brown eyes, and 26 have dark hair, brown eyes, or both. One of the boys is selected randomly. Determine the probability that he has brown eyes given that he has dark hair.
P(X)=15/23
P(X)=0.652
What does it mean if A and B are independent?
A and B are independent if the outcome of A doesn't affect the probability of B.
For Pearson's Correlation Coefficient, how would you describe the strength and direction of r=-0.9?
r=-0.9 is a strong negative correlation
A badminton club has 31 playing members. 28 play singles and 16 play doubles. Represent this as a Venn Diagram.
Only singles: 15
Only doubles: 3
Singles and doubles: 13
Outside: 0
A bag holds 3 red marbles, 5 yellow marbles, and 2 black marbles. If you grab one marble, replace it, and draw another marble, what is the probability that you draw the same color for both marbles?
P(X)=(3/10)(3/10)+(5/10)(5/10)+(2/10)(2/10)
P(X)=38/100
P(X)=19/50
P(X)=0.38
P(X)=(1/2)(4/5)/[(1/2)(2/5)+(1/2)(4/5)]
P(X)=(2/5)/(3/5)
P(X)=6/25
P(X)=0.24
You roll two dice. Find the probability that the first is odd and the second is a multiple of 3.
=(3/6)(2/6)
=(1/2)(1/3)
=1/6
What is the gradient of the line y=3x+1?
The gradient, or slope, is 3.
A survey of 21 farms showed that 15 grow crops, 9 have cattle, and and 11 have sheep. 4 have sheep and cattle, 7 have cattle and crops, and 8 have sheep and crops. 3 have cattle, sheep, and crop. Find the number of farms with only animals.
1+2+1=4
You bought 3 tickets for a raffle out of 150. There are 2 prizes that will be drawn for without replacing raffle tickets. Represent your chances of winning these prizes in a tree diagram.
2/149 win
147/149 lose
147/150 lose
3/149 win
146/149 lose
The probability Greta's mother takes her shopping is 2/5. When Greta goes shopping with her mother, she gets ice cream 70% of the time. When Greta does not go shopping with her mother she gets ice cream 30% of the time. Determine the probability that Greta went shopping with her mother, given that her mother buys her an ice cream.
P(X)=(2/5)(0.7)/[(2/5)(0.7)+(3/5)(0.3)]
P(X)=0.28/0.46
P(X)=0.609
On average, Steve runs 4 days a week. What is the probability that on 3 randomly selected days, Steve ran on all of them?
=(4/7)(4/7)4/7)
=64/343
=0.187
The gradient of L2 is the opposite reciprocal, 1/2.
A bouquet shop is arranging 40 bouquets with red, yellow, and purple flowers. 10 bouquets are using all three colors, 15 are using red and yellow, 11 are using red and purple, and 12 are using yellow and purple. There are 31 with red flowers and 21 with yellow flowers. Find the probability that a randomly selected bouquet has only purple flowers.
40-(10+1+2+5+15+4)=3
P(X)=3/40
You have a bag containing 5 purple marbles and 4 yellow marbles. You draw 3 marbles simultaneously. Find the probability that you get at least 1 purple marble.
P(X)=1-(4/9)(3/8)(2/7)
P(X)=1-24/504
P(X)=1-1/21
P(X)=20/21
P(X)=0.952
The probability that a randomly selected person has cancer is 0.02. The probability that he or she reacts positively to a test which detects cancer is 0.95 if he or she has cancer, and 0.03 if he or she does not. Determine the probability that a randomly tested person has cancer given that he or she reacts positively.
P(X)=(0.02)(0.95)/[(0.02)(0.95)+(0.98)(0.03)]
P(X)=0.019/0.0484
P(X)=0.393
The probability that 3 people score a free throw are 2/5, 1/3, and 1/2 respectively. Find the probability that at least one of them score a free throw.
=1-(3/5)(2/3)(1/2)
=1-6/30
=1-1/5
=4/5
=0.8
In triangle ABC, find a if A=63o, B=49o, and b=18cm.
a=21.3 cm