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$P(x)={_n}C_x \;P^x(1-p)^{n-x}$

*$n$: 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)

$\cdot$ binomialpdf $(n,p,x)$

$\cdot$ binomialcdf $(n,p,x)$

$x$: number of success in n trials

$p$: probability of success in each trial

$P(x)$: probability of getting $x$ successes (out of $n$ trials)

$\cdot$ binomialpdf $(n,p,x)$

$\cdot$ binomialcdf $(n,p,x)$

- 1.a)Binomialb)Binomial Formulac)Binomialpdf Calculator
- 2.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? - 3.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 - 4.A die is rolled 3 times, what is the probability that a four is rolled exactly 2 times?
- 5.A coin is flipped 20 times, what is the probability that the coin comes up heads 15 times?
- 6.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?
- 7.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.

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

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