Pascal's Triangle
From Pascal’s triangle, determine the 9th entry of the 12th row
495
Determine the coefficient of the 7th term in the binomial expansion of
(3y + x)11
112266
A coin is flipped 6 times. Assume the coin is fair. What is the probability of getting exactly 4 heads?
0.234
A standard six-sided die is rolled. Let X represent the outcome of the roll.
If you earn twice the number rolled on the die (i.e., 2X), what is your expected earnings?
7
Determine the sum of the 6th row in pascals triangle
64
From Pascal’s triangle, determine the 12th entry of the 18th row
31824
determine the third term in the binomial expansion of
(a+b)5
10a3b2
A factory produces lightbulbs, and 5% of the bulbs are defective. A batch of 10 bulbs is selected randomly.
What is the probability that exactly 2 bulbs are defective?
0.0746
You are considering two job offers. Job A has a fixed salary of $50,000 per year. Job B offers a base salary of $40,000 with a 20%20\%20% chance of earning an additional $20,000 in bonuses.
What is the expected value of the salary for Job B?
$44,000
Using Pascal's Triangle, find the coefficient of x3y2 in the expansion of (x+y)5
10
Determine the missing value using Pascal's Identity
190 1140
210 _____ 5985
1330
Expand fully
(a - b)3
A basketball player has a free-throw success rate of 80%. In a game, the player attempts 8 free throws.
What is the probability the player makes at least 7 successful throws?
0.5033
You are offered to play a game where you flip a fair coin. If it lands heads, you win $10, and if it lands tails, you lose $5.
What is the expected value of your earnings from one flip?
$2.50
A game involves rolling two fair six-sided dice. If the sum of the numbers rolled is 7, you win $10. Otherwise, you lose $2.
What is the expected value of your winnings per roll?
$0
Determine the missing value using Pascal's Identity
_________ 330
792
462
determine the 3rd term in the binomial expansion of
(2a + b)4
16a2b2
A certain disease affects 1 in 20 people in a community. A diagnostic test correctly identifies the disease with 95% accuracy. Assume 10 people from the community are randomly selected for testing.
What is the probability that exactly 2 people test positive for the disease?
0.0746
A lottery ticket costs $5. It has a 1/1000 chance of winning $5000, a 1/500 chance of winning $100, and a 1/100 chance of winning $20. All other tickets win nothing.
What is the expected net winnings of a lottery ticket?
$0.40
If from six to seven in the evening one telephone line in every five is engaged in a conversation: what is the probability that when 10 telephone numbers are chosen at random, only two are in use?
0.302
From Pascal's triangle, determine the sum of the last three values in the 12th row
Determine the 5th term in the binomial expansion of
(4w4 - 2y5)10
65,536w24y20
A company surveys 12 customers to find out if they prefer Product A. Past data shows that 70% of customers prefer Product A.
What is the probability that exactly 9 customers prefer Product A?
0.2397
An insurance company offers a life insurance policy for $100 per year. If the policyholder passes away during the year, the company pays $50,000. The probability of the policyholder passing away during the year is 0.001
What is the company's expected payout per policy?
$50
Determine the 3rd term in the binomial expansion of the following
(2a2 + 3a4)5
72a14