Binomial games
A coin is flipped 10 times whats the probability of it landing on heads 4 times and tails 6?
P(x=4)=210(0.0625)(0.015625)=0.2051
In the binomial notation, what does the value of n represent?
The number of trials.
Find P(X=4), when n=5, p=0.25, q=0.75,
P(X=4)=0.014648.
When rolling a die 50 times, what is the probability of rolling a "4" exactly 25 times?
Here n=50, p=1/6=0.1667, q=1-0.1667, k=25. Then P(X=25)=0.0000000466
What is the probability of getting heads on a fair coin?
1/2
In a bookshelf there are 200 books, 50 of which are the same book. What is the probability of choosing the same book in the bookshelf two times in a row, when randomly choosing?
P(x=2)=C(2,2)*(1/4)^2*(3/4)^0=1/16=0.0625
When solving a binomial probability, the variable X represents what?
The number of successes.
P(x=4) when n=7, p=0.4
P(x=4)=0.193536
The experiment is to roll a die 100 times, what is the probability of getting a 4 exactly 25 times?
P(X=25)=0.00982588
What is the probability of getting a 6 on fair six sided die?
1/6
Find the probability of getting exactly six "2"s in 10 rolls of a fair die.
P(x=6)=C(10,6)(1/6)^6(5/6)^4=0.00217
When solving a binomial probability the variable p represents what?
The probability of success.
P(X>=2) where n=3, p=0.5, q=0.5, R=2.
P(X>=2)=0.5
DOUBLE JEOPARDY! Create a problem that is a binomial then solve it in front of the class.
Answers will vary.
What is the probability of getting a queen in a standard 52 card deck?
4/52=1/13.
In a 15 question multiple choice test, find the probability of getting between 7 and 13 (inclusive) questions correct when randomly guessing. Assume each question has four options.
P(x<=13)-P(x<7)=.999999-.943380=0.0566202673
When solving a binomial probability, the variable q represents what?
The probability of failure.
P(5 < X < 8)=? when n=10, p=0.5
P(X<8)-P(X<=5)=0.9453125-0.6230469=0.3222656
Out of 100 students, what is the probability that between 5 to 15 of them have red hair? We can assume that the probability of a student having red hair is 10%.
The output from the binomial calculator gives us P(x<=15)-P(x<5) which gives us 96%-2%. There is a 94% chance that 5 to 15 students out of the 100 recorded will have red hair.
What is the probability of getting snake eyes (double ones) when rolling two six sided dice?
1/36
A die is rolled 3 times. What is the probability of getting at least one 2?
P(X>=1)=0.4212962963
When solving a binomial probability, the part of the equation represented by nCx represents what? (Hint: explain what is means not just the formula.)
The number of ways to choose k things from n total choices. Given by the formula n!/(X!(n-X)!).
Find P(4 < X <= 9) when n=13, q=.20
P(X<=9)-P(X<=4)=0.252675690496-0.000166006784= 0.25250968371
A Female frog lays approximately 20,000 eggs each spring. Find the probability of more than 15,000 of these eggs surviving until they are adult frogs. There is a 10% success rate of an egg surviving to adulthood. Explain your findings in context of the problem.
P(X>=15,000)=0.000001. My final answer means that there is significantly less than a 1% chance of a female frog having more than 15,000/20,000 eggs becoming adult frogs.
What is the probability of getting a Queen or a Heart when drawing a card from a shuffled deck?
16/52=4/13. There are 13 hearts and 4 queens, but one queen is also a heart.