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4 years ago

Find: P(a sophomore or student that wears glasses)

Mathematics

1 answer:

slava [35]4 years ago

5 0

Answer:

The probability is 52/83

Step-by-step explanation:

In this question, we are tasked with calculating the probability of having a student who is a sophomore or a student that wears glasses.

To do this, what we do is to first calculate the probability of having a student that is a sophomore, then calculate the probability of having a student wearing glasses. Now, considering the linking word or between the two cases, wherever we have or in probability, we are to add.

Firstly , let’s calculate the number of students we have = 6 + 13 + 5 + 27 + 9 + 23 = 83 students

The total number of sophomores we have is 5 + 27 = 32

Thus, the probability of having a sophomore is 32/83

The second case is that if a student that wears glasses. The total number of student wearing glasses is 6 + 5 + 9 = 20 students

The probability of finding a student wearing glasses is thus 20/83

Now, the probability of finding a student who wears glass or is a sophomore is 20/83 + 32/83 = 52/83

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3 years ago

Approximately 26% of all pipework failures in chemical plants are caused by operator error. What is the probability that out of

alex41 [277]

Answer:

1.17% probability that out of the next 30 pipework failures, at least 14 are due to operator error.

Step-by-step explanation:

For each pipework failure in chemical plants, there are only two possible outcomes. EIther it is caused by operator error, or it is not. For each failure, the probability of it being caused by operator failure is independent from other failures. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Approximately 26% of all pipework failures in chemical plants are caused by operator error.

This means that $p = 0.26$

What is the probability that out of the next 30 pipework failures, at least 14 are due to operator error

This is $P(X \geq 14)$ when $n = 30$

Using a binomial probability calculator, we have that

$P(X \geq 14) = 0.0117$

1.17% probability that out of the next 30 pipework failures, at least 14 are due to operator error.

7 0

3 years ago

Ifƒ(x ) = 3x + 1 and ƒ -1 = (x-1)/3, then ƒ(2) = A) 1/3 B) 1 C) 7

Vikentia [17]

The problem gave us the equation for $f(x)$ , which was $f(x) = 3x + 1$ . To find $f(2)$ , we can simply substitute 2 in for $x$ , as shown below:

$f(2) = 3(2) + 1 = 7$

The answer is f(2) = 7.

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3 years ago

Paula has a dog that weighs 3 times as much as Carla's dog. The total weight of the dogs is 48 pounds. How much does Paula's dog

spayn [35]

Let the weight of Paula's dog be x
Let the weight of Carla's dog be y

We know that the weight of Paula's dog is 3 times that of Carla's dog, therefore:
x = 3y ...........> equation I

We also know that the sum of the weights is 48 pounds, therefore:
x + y = 48 ............> equation II

Substitute with equation I in equation II:
3y + y = 48
4y = 48
y = 12 pouds

Substitute with the value of y in equation I:
x = 3(12) = 36 pounds

Based on the above calculations:
Paula's dog weighs 36 pounds
Carla's dog weighs 12 pounds

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3 years ago

Kiran starts at 9:00 am by bicycle to reach office. She cycles at the speed of 8 km/hour and reaches the office at 9:15 am. By h

Ivenika [448]

Answer:

v = 12 km/h

Step-by-step explanation:

To find how much she should increase the speed first we need to find the distance traveled:

$d = v*t$

Where:

d: is the distance traveled =?

v: is the velocity = 8 km/h

t: is the time = 15 min (9:00 to 9:15)

$d = v*t = 8 km/h*15 min*\frac{1 h}{60 min} = 2 km$

Now, we can find the speed:

$v_{f} = \frac{d}{t} = \frac{2 km}{10 min*\frac{1 h}{60 min}} = 12 km/h$

Therefore, she should increase the speed to 12 km/h to reach the office at 9:10 am.

I hope it helps you!

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3 years ago