Ask question

Ask question

All categories

3 years ago

11

A box in a supply room contains 22 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 5 are

rated 23-watt. Suppose that three of these bulbs are randomly selected. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?
(b) What is the probability that all three of the bulbs have the same rating?
(c) What is the probability that one bulb of each type is selected?
(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

1 answer:

miskamm [114]3 years ago

8 0

Answer:

a)P(exactly 2 bulb from watt)= 0.11

b)P=0.097

c)P=0.233

d)P=0.235

Explanation:

Total bulb = 22

13 watt bulb = 8

18 watt = 9

23 watt = 5

We have to select 3 bulb out of 22 bulb

We know that probability is the ratio of favor condition to the total condtion.

The total number of way to select 3 bulb out of 22 =N

$N=_{3}^{22}\textrm{c}$

a)

$P(exactly\ 2\ bulb\ from\ 23\ watt)= \dfrac{_{2}^{5}\textrm{c}._{1}^{17}\textrm{c}}{_{3}^{22}\textrm{c}}$

$P(exactly\ 2\ bulb\ from\ 23\ watt)= \dfrac{170}{1540}$

P(exactly 2 bulb from watt)= 0.11

b)

The probability that all three of the bulbs have the same rating =P

$P=\dfrac{_{3}^{5}\textrm{c}+_{3}^{8}\textrm{c}+_{3}^{9}\textrm{c}}{_{3}^{22}\textrm{c}}$

$P= \dfrac{150}{1540}$

P=0.097

c)

The probability that one bulb of each type is selected=P

$P=\dfrac{_{1}^{5}\textrm{c}._{1}^{8}\textrm{c}._{1}^{9}\textrm{c}}{_{3}^{22}\textrm{c}}$

$P= \dfrac{360}{1540}$

P=0.233

d)

The probability that it is necessary to examine at least 6 bulbs =P

$P=\dfrac{_{5}^{17}\textrm{c}}{_{5}^{22}\textrm{c}}$

$P= \dfrac{6188}{26334}$

P=0.235

You might be interested in

How does a comet change as it travels through space

AfilCa [17]

Comets are like "dirty snowballs"; frozen gasses with dust and rocks in them. Each pass near the Sun causes the comet's nucleus to be exposed to intense sunlight, which causes some tiny fraction of the gas to evaporate and carry some of the dust and rock away into space. The gas and dust, near the Sun, cause the comet's "tail", and repeated passes cause dust and rock to spread out along most of the orbit of a comet. When the Earth enters one of these trails of old comet dust, we have meteor showers.

<span>On rare occasions, comets break apart or even more rarely, crash into planets. In 1994, the comet Shoemaker-Levy 9 broke apart and then collided with the planet Jupiter.</span>

5 0

3 years ago

In 3 seconds a car moving in a straight line increases its speed from 22.4 m/s to 29.1 m/s while a truck increases its speed fro

ANTONII [103]

Is there a picture?

6 0

3 years ago

A series AC circuit contains a resistor, an inductor of 150 mH, a capacitor of 5.00 mF, and a generator with DVmax 5 240 V opera

yanalaym [24]

Given:

Inductance, L = 150 mH

Capacitance, C = 5.00 mF

$\Delta V_{max}$ = 240 V

frequency, f = 50Hz

$I_{max}$ = 100 mA

Solution:

To calculate the parameters of the given circuit series RLC circuit:

angular frequency, $\omega$ = $2\pi f = 2\pi \times50 = 100\pi$

a). Inductive reactance, $X_{L}$ is given by:

$\X_{L} = \omega L = 100\pi \times 150\times 10^{-3} = 47.12\Omega$

$X_{L} = 47.12\Omega$

b). The capacitive reactance, $X_{C}$ is given by:

$\X_{C} = \frac{1}{\omega C} = \frac{1}{2\pi fC} = \frac{1}{2\pi \times 50\times 5.00\times 10^{-3}} = 0.636\Omega$

$X_{C} = 0.636\Omega$

c). Impedance, Z = $\frac{\Delta V_{max}}{I_{max}} = \frac{240}{100\times 10^{-3}} = 2400\Omega$

$Z = 2400\Omega$

d). Resistance, R is given by:

$Z = \sqrt {R^{2} + (X_{L} - X_{C})}$

$2400^{2} = R^{2} + (47.12 - 0.636)^{2}$

$R = \sqrt {5757839.238}$

$R = 2399.5\Omega$

e). Phase angle between current and the generator voltage is given by:

$tan\phi = \frac{X_{L} - X_{C}}{R}$

$\phi =tan^{-1}( \frac{X_{L} - X_{C}}{R})$

$\phi =tan^{-1}( \frac{47.12 - 0.636}{2399.5}) = tan^{-1}{0.0.01937}$

$\phi = 1.11^{\circ}$

5 0

4 years ago

A boat takes off from a dock at 2.5 m/s and speeds up at 4.2 m/s squared for six seconds how far has the most traveled

GaryK [48]

The boat's position $x$ relative to its starting point $x_0=0$ is determined by

$x=x_0+v_0t+\dfrac12at^2$

where $v_0$ is its initial velocity, $a$ is its acceleration, and $t$ is time. After $t=6\,\mathrm s$ , the boat has traveled

$x=\left(2.5\,\dfrac{\mathrm m}{\mathrm s}\right)(6\,\mathrm s)+\dfrac12\left(4.2\,\dfrac{\mathrm m}{\mathrm s^2}\right)(6\,\mathrm s)^2$

$\implies x=91\,\mathrm m$

3 0

3 years ago

What is the size of earth?

shtirl [24]

Answer:

Google it

Explanation:

Best if you use google

4 0

3 years ago

Read 2 more answers