Given:
1 - 50 written in red marker
51 - 100 written in blue marker

Probability of selecting a number greater than 81; 100 - 81 = 19 possible numbers. 1 draw. 1/19

Probability of selecting a number written in red: 1/50

Probability of selecting a number written in blue: 1/50

Probability of selecting a number that is a multiple of 10. There are 10 instances; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 ; 1/10

5 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

Mazyrski [523]

Answer:

The probability that the instrument does not fail in an 8-hour shift is $P(X=0) \approx 0.8659$

The probability of at least 1 failure in a 24-hour day is $P(X\geq 1 )\approx 0.3508$

Step-by-step explanation:

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

$P(X)=\frac{e^{-\mu}\mu^x}{x!}$

Let X be the number of failures of a testing instrument.

We know that the mean $\mu = 0.018$ failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:

For an 8-hour shift, the mean is $\mu=8\cdot 0.018=0.144$

$P(X=0)=\frac{e^{-0.144}0.144^0}{0!}\\\\P(X=0) \approx 0.8659$

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:

For a 24-hour day, the mean is $\mu=24\cdot 0.018=0.432$

$P(X\geq 1 )=1-P(X=0)\\\\P(X\geq 1 )=1-\frac{e^{-0.432}0.432^0}{0!}\\\\P(X\geq 1 )\approx 0.3508$

3 0

3 years ago

Help. also explain :) please

Anuta_ua [19.1K]

The answer is £140

First you find 20% of 1200 (which is basically 20 times 12) which gives you £240.

You add £240 to £1200 which is £1440

Then you take £300 off £1440 since he already paid the deposit.

That leaves you with £1140

1140 divided by 10 is 114

5 0

2 years ago