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tensa zangetsu [6.8K]
3 years ago
7

a town has 2 fire engines operating independently . the probability that a specific engine is available when needed is 0.96. wha

t is the probability that neither is available when needed
Mathematics
1 answer:
tester [92]3 years ago
7 0

Answer:

The probability that neither is available when needed

P(A n B)^{c} = 0.04  

Step-by-step explanation:

A town has 2 fire engines operating independently

Given data  the probability that a specific engine is available when needed is 0.96.

Let A and B are the two events of two fire engines

given  P(A and B) = 0.96 ( given two engines are independent events so you have to select A and B)

Independent events : P( A n B) = P(A) P(B)

The probability that neither is available when needed

P(A n B)^{c} = 1- P(A n B)

P(A n B)^{c} = 1- 0.96 = 0.04

                                     

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A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is u
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==========================

How I got that answer:

Draw out a line segment and label it to be 40 meters long. Somewhere in the middle (not the exact midpoint necessarily), draw a cutting line to divide the segment into two (not necessarily equal) parts. The first part is x units long. The remaining bit is 40-x units long. See the attached image below. The drawing is optional, but it might help to visually see how the two parts interact.

------------

The wire that is x units long is used to form a circle of radius r. The question is: what is x in terms of r?

The circumference of the circle of radius r is

C = 2*pi*r

If we cut the circle and unroll it out into a straight line, then its perimeter or circumference will stretch into a line of length 2*pi*r. So this must be the length of x.

x = 2*pi*r

-----------

The value of 40-x is then

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The total perimeter of the square is P = 4*s, where s is the side length. Solving for s gets to

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Plug in P = (40-2pi*r) and simplify

s = P/4

s = (40-2pi*r)/4

s = 40/4-(2pi*r)/4

s = 40/4-(2/4)pi*r

s = 10 - (1/2)pi*r

----------

We know the side length of the square, which can be used to find the area of the square

A = area of square

A = s^2

A = (10-(1/2)*pi*r)^2

----------

M = area of circle = pi*r^2

N = area of square = (10-(1/2)*pi*r)^2

total area = M+N

total area = pi*r^2 + (10-(1/2)*pi*r)^2

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