Mathematics, 16.03.2020 22:43 theblackdot16

Police records in the town of Saratoga show that 15 percent of the drivers stopped for speeding have invalid licenses. If 12 drivers are stopped for speeding, (a) Find the probability that none will have an invalid license. (Round your answer to 4 decimal places.) P(X = 0) (b) Find the probability that exactly one will have an invalid license. (Round your answer to 4 decimal places.) P(X = 1) (c) Find the probability that at least 2 will have invalid licenses. (Round your answer to 4 decimal places.) P(X ≥ 2)

Answers: 2

Show answers

Answers

Answer from: lesgumball

a) $P(X=0) = (12C0) (0.15)^0 (1-0.15)^{12-0} =0.1422$

b) $P(X=1) = (12C1) (0.15)^1 (1-0.15)^{12-1} =0.3012$

c) $P(X \geq 2) = 1-P(X$

And replacing we got:

$P(X \geq 2)= 1- [0.1422+0.3012]= 0.5566$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=12, p=0.15)$

Part a

We want this probability:

$P(X=0) = (12C0) (0.15)^0 (1-0.15)^{12-0} =0.1422$

Part b

We want this probability:

$P(X=1) = (12C1) (0.15)^1 (1-0.15)^{12-1} =0.3012$

Part c

We want this probability:

$P(X \geq 2)$

And we can use the complement rule:

$P(X \geq 2) = 1-P(X$

And replacing we got:

$P(X \geq 2)= 1- [0.1422+0.3012]= 0.5566$

Answer from: Quest

step-by-step explanation:

so first find out how much each is worth.

quarter= 25 cents

dime= 10 cents

pennies= 1 cent

then multiply each by how much each is worth.

200 150 300

x x x 1

25 10

300

1000 1500

4000

5000

then count 2 from the back and add a period.

$50.00

$15.00

$3.00

and then add them

$50.00

$15.00

$3.00

$68.00

so sunghee has $68.00

Another question on Mathematics

Mathematics, 21.06.2019 21:50

Which rule describes the composition of transformations that maps ajkl to aj"k"l"? ro. 900 o to, -2(x, y) to, -20 ro, 900(x, y) ro, 9000 t-2. o(x,y) t-2, 00 ro, 900(x, y)

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Let u = {q, r, s, t, u, v, w, x, y, z} a = {q, s, u, w, y} b = {q, s, y, z} c = {v, w, x, y, z}. list the elements in the set.a ∩ (b ∪ c)a) {q, s, w, y}b) {q, y, z}c) {q, s, u, w, y, z}d) {q, r, w, y, z}

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

Rewrite the equation x = 65 - 60p by factoring the side that contains the variable p.

Answers: 2

Answer

Mathematics, 22.06.2019 01:30

Subject: geometryneed with 6 and 7

Answers: 2

Answer

You know the right answer?

Police records in the town of Saratoga show that 15 percent of the drivers stopped for speeding have...