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Binomial distribution
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Binomial distribution
Lessons
P(x)=nCxPx(1−p)n−x
n: number of trials
x: number of success in n trials
p: probability of success in each trial
P(x): probability of getting x successes (out of n trials)
⋅ binomialpdf (n,p,x)
⋅ binomialcdf (n,p,x)
n: number of trials
x: number of success in n trials
p: probability of success in each trial
P(x): probability of getting x successes (out of n trials)
⋅ binomialpdf (n,p,x)
⋅ binomialcdf (n,p,x)
- Introductiona)Binomialb)Binomial Formulac)Binomialpdf Calculator
- 1.Identify which of the following experiments below are binomial distributions?
i. A fair die is rolled 4 times. What is the probability of the one coming up 2 times?
ii. A fair coin is flipped until head comes up 7 times. What is the probability that the coin will be flipped 10 times?
iii. 1,000,000 nails are produced in a factory a day. If each nail has a probability of 0.5% of being defective (something being wrong with that nail), then what is the probability that less than 50 nails will be defective in a day?
iv. Roughly 7.5% of Canadians have some form of heart disease. If 100 Canadians are sampled what is the probability that 10 of them will have heart disease?
v. If 5 cards are drawn from a deck, what is the probability that 2 of them will be hearts?
vi. If a fair die is rolled 8 times, what is the probability of getting 2 fours and 3 sixes? - 2.An urn contains 6 red balls and 4 green balls. A total of 5 balls are drawn; list all the different combinations of red balls that can be drawn in each of the following cases:
i. A total of 3 green balls are drawn
ii. At most 3 red balls are drawn
iii. At least 2 red balls are drawn
iv. Less than 4 red balls are drawn
v. More than 3 green balls are drawn - 3.A die is rolled 3 times, what is the probability that a four is rolled exactly 2 times?
- 4.A coin is flipped 20 times, what is the probability that the coin comes up heads 15 times?
- 5.Jimmy the Joker is an unfair gambler. He weights a die so it rolls a "6" with 75% chance. He then bets that if he rolls his die 4 times he will roll six exactly 3 times. What is his probability of winning this bet?
- 6.Thomas is packing for a trip and wants to bring some stuffed animals along for comfort. He owns 8 stuffed animals, and will pack each stuffed animals independently of all the others with a probability of 30%. Determine the probability that he takes;a)0 stuffed animals along with him.b)1 stuffed animal with himc)at most two animals along with him.d)at most 5 animals along with him.e)at least 6 animals along with him.
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4.
Discrete Probabilities
4.1
Probability distribution - histogram, mean, variance & standard deviation
4.2
Binomial distribution
4.3
Mean and standard deviation of binomial distribution
4.4
Poisson distribution
4.5
Geometric distribution
4.6
Negative binomial distribution
4.7
Hypergeometric distribution
4.8
Properties of expectation