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Verdich [7]9 months ago

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A candy dish contains 30 jelly beans and 20 gumdrops. Ten candies are picked at random. What is the probability that 5 of the 10

AveGali [126]

Answer:

The probability of drawing 5 gumdrops in 10 picks from the dish is 0.215

Step-by-step explanation:

A hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws with each draw being a success or failure, without replacement from a finite population size that contains exactly the same objects. The general formula is given as:

$h(x) =\frac{({A}C_{x})({N-A}C_{n-x})}{^{N}C_{n} }$

where:

$^{n}C_{r}=\frac{n!}{(n-r)!r!}$

h(x) is the probability of x successes,

n is the number of attempts,

A is the number of successes

N is the number of elements

For this problem:

A = 30, x = 5, N = 50, n = 10

The probability of drawing 5 gumdrops in 10 picks from the dish P(x=5) is

$P(x=5)=\frac{({30}C_{5})({50-30}C_{10-5})}{^{50}C_{10} }\\P(x=5)=\frac{({30}C_{5})({20}C_{5})}{^{50}C_{10} }$

$P(x=5)=\frac{\frac{30!}{(30-5)!5!}*\frac{20!}{(20-5)!5!} }{\frac{50!}{(50-10)!10!} }\\P(x=5)=\frac{\frac{30!}{25!5!}*\frac{20!}{15!5!} }{\frac{50!}{40!10!} }$

$P(x=5)=\frac{142506*15504}{1.207*10^{10} }=0.215$

P(x=5) = 0.215

The probability of drawing 5 gumdrops in 10 picks from the dish is 0.215

4 0

3 years ago

A woman who weighs 160 pounds on earth weighs 30 on the moon. If a boy weighs 60 pounds on earth , how much dose he weigh on the

Igoryamba

60Kg. Mass does not vary by the strength of the gravitational field. What changes is the weight which will only be about one-sixth of what it is on Earth. So a 60Kg mass on the Moon would weigh approximately the same as a 10Kg mass on the Earth.

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2 years ago

Read 2 more answers

What is 20-6n=-2(n+6)?

blsea [12.9K]

20n - 6n = -2(n + 6)

20 - 6n =-2n -12

6n + 2 n = -20 -12

8n = 32

n = 32 : 8

n = 8

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