What is36.8+[11.6-(2.5×3)]2

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

1 year ago

Use the model below to estimate the average annual growth rate of a certain country's population for 1950, 1988, and 2010, where

Morgarella [4.7K]

Answer:

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 2.398, 0.9985 and 0.2236 respectively.

Step-by-step explanation:

The given equation is

$Y=-0.0000084x^3+0.00211x^2-0.205x+8.423$

Where Y is the annual growth rate of a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

$Y=-0.0000084(50)^3+0.00211(50)^2-0.205(50)+8.423$

$Y=2.398$

Therefore the estimated average annual growth rate of the country's population for 1950 is 2.398.

Difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

$Y=-0.0000084(88)^3+0.00211(88)^2-0.205(88)+8.423$

$Y=0.9984752\approx 0.9985$

Therefore the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

$Y=-0.0000084(110)^3+0.00211(110)^2-0.205(110)+8.423$

$Y=0.2236$

Therefore the estimated average annual growth rate of the country's population for 2010 is 0.2236.

8 0

3 years ago

Question 1 of 5<br>Find the greatest common factor of these three expressions<br>12y,8y", and 20 y?

rewona [7]

Answer: 4y is the greatest common factor

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Logan paid 2.16 dollars for 3 lollipops. Each lollipop cost c cents. Create an equation and solve to find the cost of one lollip

Nutka1998 [239]

We can set up the equation as follows:
3c = 2.16, and dividing by 3 on both sides, we get:
c = 0.72.
Each lollipop cost 72 cents.
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Hope this helps!
==jding713==

4 0

3 years ago

Read 2 more answers

In chemistry a mole is a unit of measure equal to 6.02x10^23 atoms of a substance. The mass of a single neon atom is about 3.35x

Slav-nsk [51]

2(6.02*10^23)(3.35*10^-23)

2*6.02*3.35

answer : 4.0334*10^1

7 0

3 years ago