Probability
What is the probability of rolling a 6 on a standard six-sided die?
1/6 or 0.1667
8 people locked in a room take turns holding hands with each person only once. How many hand holdings take place?
28
What's the formula for caculating the total number of combinations when choosing K items from a set of N items?
n! (K! * (n-k)!)
g(n)=n2 +4+2n
h(n)=-3n+2
Find (g×h)(1)
-7
A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow?
3 feet long
What is the probability of flipping a fair coin three times in a row and getting heads each time?
1/8 or 0.125
A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?
96
How many different committees of 4 people can be formed from a group of 10 people?
210 different committees
h(x)=3x+3
g(x)=-4+1
Find (h+g) (10)
-6
A 40-foot flagpole casts a 25-foot shadow. Find the shadow cast by a nearby building 200 feet tall
125 feet long
A bag contains 5 red balls and 7 blue balls. What is the probability of drawing a red ball from the bag without replacement?
5/12 or 0.4167
If a series of license plates is to be produced that all have the same pattern of three letters followed by three numbers, roughly how many alphanumeric combinations are possible?
26,000
How many different 5-card hands can be dealt from a standard deck of 52 cards?
2,598,960
g(x)=2x-5
h(x)=4x+5
Find g(3)-h(3)
-16
A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower?
2.4 meters
A box contains 4 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a blue ball from the box if you draw a red ball and do not replace it?
3/8 or 0.375
If there are 8 points in a plane, and no 3 of the points lie along the same line, how many unique lines can be drawn between pairs of these 8 points?
28
How many ways can 5 different book be arranged on a shelf?
120 ways
g(n)=3n+2
f(n)=2n2+5
Find g(f(2))
337
A tree with a height of 4m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 20 m long?
5.33 meters
A jar contains 10 red candies and 15 blue candies. What is the probability of randomly drawing a blue candy from the jar and then drawing another blue candy from the jar without replacement?
0.35
Mark has 5 pants and 7 shirts in his closet. He wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. How many weeks can he do this for?
5
In how many ways can 8 people be seated in a row of 8 chairs if 3 specific people refuse to sit next to each other?
2,520 ways
h(n)=4n+5
g(n)=3n+4
Find (h-g)(n)
0
Luisa began walking up a hill at a spot where the elevation is 0.9 km. After she walked 3 km, she saw a sign giving the elevation as 0.95 km. How far will she have walked when she reaches and elevation of 1.1 km?
1.1 km