judgmentnight

Candy

February 4, 2010

Candy (2006) IMDB rating: 8.00 Plot: This story is a narration from an Australian man who falls in love with two kinds of Candy: a woman of the same name and heroin. The narrator changes from a smart-aleck to someone trying to find a vein to inject, while Candy changes from an actress, call girl, streetwalker, and then a madwoman. Starting in Sydney, the two eventually end up in Melbourne to go clean, but they fail. This leads them to turn to finding money and heroin, while other posessions and attachments become unimportant.

Actors: Ledger Heath,Rush Geoffrey,Budge Tom,Meza-Mont Roberto,Martin Tony,Moraghan Craig,Lee John,Herriman Noel,McKenzie Tim,Drama,

Data and probability help please!?
This is a homework question i have for my data class. 30% of candies produced by a company are red candies. Packages of 10 are randomly selected. What is the probability that less than 3 candies in a box are red?
Considering the candies have no specific order is it not correct to do..
(0.3)^2 * (0.7) ^8 + (0.3)^1 * (0.7) ^9 + (0.7) ^10

However, I’m wondering if combinations must be used…

10C2 (0.3)^2 * (0.7) ^8 + 10C1(0.3)^1 * (0.7) ^9 + * (0.7) ^10

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Let X be the number of red candies in the box. X has the binomial distribution with n = 10 trials and success probability p = 0.3

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, …, n
P[X = x] = 0 for any other value of x.

The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.

X ~ Binomial( n = 10 , p = 0.3 )

the mean of the binomial distribution is n * p = 3
the variance of the binomial distribution is n * p * (1 - p) = 2.1
the standard deviation is the square root of the variance = v ( n * p * (1 - p)) = 1.449138

The Probability Mass Function, PMF,
f(X) = P(X = x) is:

P( X = 0 ) = 0.02824752
P( X = 1 ) = 0.1210608
P( X = 2 ) = 0.2334744
P( X = 3 ) = 0.2668279
P( X = 4 ) = 0.2001209
P( X = 5 ) = 0.1029193
P( X = 6 ) = 0.03675691
P( X = 7 ) = 0.009001692
P( X = 8 ) = 0.001446701
P( X = 9 ) = 0.000137781
P( X = 10 ) = 5.9049e-06

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3827828
Merlyn | Feb 03, 2010

Entry Filed under: Uncategorized. Tags: 2006, Budge Tom, Drama, Herriman Noel, Ledger Heath, Lee John, Martin Tony, McKenzie Tim, Meza-Mont Roberto, Moraghan Craig, Rush Geoffrey.