Combinations and Binomial Theorem
Pascal's Triangle
Probability Distribution
Binomial Probabilities
Binomial Probability Distribution
100
A jar contains 10 marbles. It contains 3 blue marbles, 4 white marbles, and 3 green marbles. If you pick 5 marbles, what is the probability of choosing exactly 2 white marbles?
( ((4),(2)) ((6),(3)))/(((10),(5)))
100
What is the sum of the 7th row in Pascal's Triangle?
2^7 = 128
100
What is the total height of the bars in a histogram for a probability distribution?
1
100
How many possible outcomes are there in a binomial experiment?
2
100
As n increases, how does the graph of a binomial probability distribution change?
the graph flattens and "spreads out"; the maximum value decreases
200
Pete's A Pizza restaurant menu lists 15 different toppings. How many different pizzas could be ordered with 6 toppings?
((15),(6)) = 5,005
200
What are the last two terms in row 21 of Pascal's Triangle?
21, 1
200
What is the mode?
2
200
A softball player's batting average is 0.344. What is the probability she gets exactly 3 hits during 4 at-bats?
((4),(3)) (0.344)^3(0.656) = 0.107
200
As p increases from 0 to 1, what happens to the graph of the binomial probability distribution?
the graph shifts from skew left to skew right
300
Expand:
(x+y)^5
x^5 + 5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5
300
What is the 6th term in row 15 of Pascal's Triangle?
3,003
300
What is the mean of the random variable?
0.98
300
Consider tossing a coin 10 times. Find the probability of getting exactly 6 heads if the coin is fair. Round to the nearest thousandth.
0.205
300
A basketball player's free throw percentage is 65%. What is the probability the player makes at most 7 shots out of 10 attempted shots? Round to the nearest hundredth.
binomcdf(10, 0.65, 7) = 0.738
400
Expand:
(3+2x)^3
27+54x+36x^2+8x^3
400
What are the first four terms in row 13 of Pascal's Triangle?
1, 13, 78, 286
400
In a Binomial Experiment, there are 300 trials and the probability of success is 0.73. What is the mean of the random variable?
219
400
Determine the probability that there are exactly 3 ones in 10 tosses of a fair 6-sided die.
((10),(3)) (1/6)^3(5/6)^7 = 0.155
400
A basketball player's free throw percentage is 65%. What is the probability the player makes at least 7 shots out of 10 attempted shots? Round to the nearest hundredth.
1 - binomcdf(10,0.65,6) = 0.514
500
Find the term containing
x^4
(x-3)^7
-945x^4
500
The sum of the elements in one of the rows of Pascal's Triangle is 4,096. What row is this?
the 12th row
500
In a binomial experiment, there are 55 trials and the probability of success is 0.65. What is the standard deviation of the random variable? Round your answer to the nearest hundredth
3.54
500
A baseball player has a batting average of 0.250. Find the probability that this batter gets at least 4 hits in 5 at-bats.
((5),(4)) (0.25)^4(0.75)+((5),(5))(0.25)^5=0.015625
500
Let p = 0.8. Draw a graph of the binomial probability distribution for n = 4.
Enter into L1 : 0, 1, 2, 3, 4
into L2: binompdf(4, 0.8)
Then, graph.