What is an equation for the scenario the entrance fee to an amusement park is $9 plus $1.50 for each ride

A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five

exis [7]

Answer:

$\dfrac{14}{29}$

Step-by-step explanation:

Let P(A) be the probability that goggle of type A is manufactured

P(B) be the probability that goggle of type B is manufactured

P(E) be the probability that a goggle is returned within 10 days of its purchase.

According to the question,

P(A) = 30%

P(B) = 70%

P(E/A) is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.

P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.

$P(A \cap E)$ will be the probability that a goggle is of type A and is returned within 10 days of its purchase.

$P(B \cap E)$ will be the probability that a goggle is of type B and is returned within 10 days of its purchase.

$P(E \cap A) = P(A) \times P(E/A)$

$P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%$

$P(E \cap B) = P(B) \times P(E/B)$

$P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%$

$P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%$

If a goggle is returned within 10 days of its purchase, probability that it was of type B:

$P(B/E) = \dfrac{P(E \cap B)}{P(E)}$

$\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}$

So, the required probability is $\dfrac{14}{29}.$

7 0

3 years ago

You want to put $4,000 in a simple interest account. It has a 2.5% annual interest rate. How long will it take you to earn $500

SVEN [57.7K]

Answer:

5 years

Step-by-step explanation:

use the I = Prt simple interest formula

8 0

3 years ago

Emails arrive at the server of a company at the rate of an average of 10 per hour. It is assumed that a Poisson process is a goo

fomenos

Answer:

0.37

Step-by-step explanation:

we have given that emails arrives at the server at the rate of 10 per hour means $\frac{10}{60}=0.166$ per minute

we have to find the probability that the time difference between the two email is more than 2 minute

so probability $P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166$

4 0

3 years ago

The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m

photoshop1234 [79]

Answer: 0.1353

Step-by-step explanation:

Given : The mean of failures = 0.025 per hour.

Then for 8 hours , the mean of failures = $\lambda=8\times0.25=2$ per eight hours.

Let X be the number of failures.

The formula to calculate the Poisson distribution is given by :_

$P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}$

Now, the probability that the instrument does not fail in an 8-hour shift :-

$P(X=0)=\dfrac{e^{-2}2^0}{0!}=0.1353352\approx0.1353$

Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353

7 0

3 years ago

1. What is the standard form for the following: 3x^2 - 4x + 6x^5 + 10x^3 - 8

Mrrafil [7]

Answer:

how this helps

Step-by-step explanation:

6 0

3 years ago