What is birthday paradox?Explain with it an example.what is the probability of finding a collision for an ideal 60 bit hash function?what is the main reason for this probability?

The population proportion is .60. What is the probability that a sample proportion will be within +/- .02 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places.

n=100

n=200

n=500

n=1000

If a license plate has four different digits on it, what is the probability that the numbers on the plate will not be in either consecutive increasing or consecutive decreasing order? Show you work.

The population proportion is 0.26. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? (Round your answers to 4 decimal places.)

(a)

n = 100

(b)

n = 200

(c)

n = 500

(d)

n = 1,000

(e)

What is the advantage of a larger sample size?

There is a higher probability

σ_p

will be within ±0.04 of the population standard deviation.We can guarantee

p

will be within ±0.04 of the population proportion p.    As sample size increases,

E(p)

approaches p.There is a higher probability

p

will be within ±0.04 of the population proportion p.

b. Calculate the probability that 31​% or more of the sample will be living in poverty. Assume the sample is collected in such a way that the conditions for using the CLT are met. Upper P left parenthesis Modifying Above p with caret greater than or equals 0.31 right parenthesis equals nothing ​(Round to three decimal places as​ needed.)

2. In a group of 5 teenagers, what is the probability that at least two of them were born in the same year?

whats the probability of rolling a 1 or 5 but not both on two rolls