Calculate the expected value given
x | 1 | 2 | 4 |
p(x) |1/5|2/5|1/5|
What is E(x) = (1/5)*1+(2/5)*2 + (1/5)*4 = 1.8
100
P(a and b) = P(a) * P(b)
P(a) = 1/4
P(b) = 2/4
P(a)*P(b)= ?
What is (1/4)*(2/4) = 2/8
100
P(a or b) = P(a) + P(b)
P(a) = 4/8
P(b) = 1/8
P(a) + P(b) = ?
What is 4/8+1/8 =5/8
100
how many ways unique ways can you arrange the numbers 4,3,2,1,6?
What is 5! =5*4*3*2*1 = 120
200
Calculate 7 nCr 4
What is 7!/{(7-4)!4!} = 35
200
You win 2 dollars if you flip a heads and you loose 3 dollars if you flip a tails. What is your expected value if you play this game?
What is E(x) = (1/2)*(-2) + (1/2)*3 = $1/2
200
The probability of flipping a heads and then another heads
What is (1/2)*(1/2) = 1/4
200
what is the probability of rolling a 1,2 or 3?
What is 1/6+1/6+1/6 = 3/6
200
a hat contains 12 numbers inside of it. what is the probability of selecting a number that is greater then 6 and divisible by 3?
What is numbers 9 and 12, = 2/12
300
I have a choice to choose 4 paints from a box, what are all the unique ways I can hang them on my wall?
What is = 4! = 4*3*2*1 = 24
300
you are given a spinner that has 4 choices on it. If you spin a 1 you win $2, if you spin a 2 or a 3 win $3, if you spin a 4 you loose $4. what is your expected value?
What is E(x) = 1/4*(2) + 2/4*(3) + 1/4*(-4) = $1
300
There are 3 cymbals and 2 snare drums in a closet. what is the probability of pulling a cymbal out and then another one without replacing the first?
What is 3/5*2/4 = 6/20
300
There are 4 milk shake flavors on a menu S={strawberry, cherry, vanilla, chocolate}
What is the probability of selecting either strawberry or chocolate?
What is 1/4 + 1/4 = 2/4
300
There are 15 supermodels trying out for a fashion show how many unique ways can they align themselves on the runway?
What is 15P5 =360,360
400
There are 6 runners who compete in a race what are all the ways we can assign 1st, 2nd, 3rd, and 4th place?
What is 6P4 = 6!/(6-4)! = 360
400
A horse has a 1 in 10 chance of finishing 1st and wins $2000 dollars. If he looses the owner has to pay $500. What is the expected value?
What is E(X) = (1/10)*(2000) + (9/10)(-500) = -$250
400
what is the probability of rolling three 6's in a row given a fair six sided cube?
What is 1/6*1/6*1/6 = 1/216
400
there are 6 red, 4, green and 5 blue marbles in a bag? what is the probability of selecting a red or blue marble from the bag?
What is 6/15+5/15 = 11/15
400
A car has a 1/3 chance of getting stuck in 2 feet of mud, a 1/3 chance of sinking 4 feet in quick sand and a 1/3 chance of bouncing itself 8 feet in the air with shocks. What is the cars expected height?
What is (1/3)*-2 +(1/3)*-4 + (1/3)*8 = 2/3
500
A Football team has 15 players on its roster. Only 12 players can be on the court at one time. How many different groups of 12 players can the team put on the floor?
What is 15C12 = 15!/((15-12)!*12!) =455
500
A cat has a 1/5 chance of eating 2 lbs of food, 2/5 chance of eating 3 lb of food, and 2/5 chance of throwing up 1 lb of food. what is the cats expected value of food it will consume?
What is E(x) = (1/5)*2 + (2/5)*3 + (2/5)*-1 = -1.2
500
There are 3 basketballs, 2 golf balls and 4 tennis balls in a bag. what is the probability of pulling a basketball, a tennis ball and a golf ball without replacing any of them?
What is (3/9)*(4/8)*(2/7) = 24/504
500
A magic hen can lay 6 red eggs, 3 blue eggs, and 7 green eggs in one day. what is the probability of selecting a red, blue or green egg from the bag?