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UkoKoshka [18]
2 years ago
13

A fair cubical die is thrown four times. use the binomial probability formula to calculate the probability of at least two 3's.

Engineering
1 answer:
Marina86 [1]2 years ago
6 0

By using the binomial probability formula, the probability of at least two 3's is equal to 0.1319.

<h3>How to calculate the probability of at least two 3's?</h3>

Since the fair cubical die is thrown four times, the number of times is given by n = 4 and the probability of 3's is P = 1/6.

Mathematically, the binomial probability formula is given by:

P(X \geq x) =\sum^{n}_{r=x} ^nC_r (p)^r (q)^{(n-r)}\\\\P(X \geq 2) = \; ^4C_2 (\frac{1}{6} )^2 (\frac{5}{6} )^{(4-2)} + ^4C_3 (\frac{1}{6} )^3 (\frac{5}{6} )^{(4-3)} + ^4C_4 (\frac{1}{6} )^4 (\frac{5}{6} )^{(4-4)}\\\\P(X \geq 2) = 6 \times \frac{1}{36} \times \frac{25}{36} + 4 \times \frac{1}{216} \times \frac{5}{36} + 1 \times \frac{1}{1296} \times 1\\\\P(X \geq 2) =  \frac{150}{1296} +  \frac{20}{1296}+  \frac{1}{1296}

P(X ≥ 2) = 19/144

P(X ≥ 2) = 0.1319.

Read more on probability here: brainly.com/question/25870256

#SPJ1

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A cylindrical metal specimen having an original diameter of 10.55 mm and gauge length of 54.5 mm is pulled in tension until frac
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Answer:

(a) 53.94%

(b) 26.61%

Explanation:

Change in area will be given by

\triangle A=\frac {\pi(R_o^{2}-r_n^{2})}{\pi R_o^{2}} where \triangle A represent change in area R is radius and subscripts O and n represent original and new respectively.

Substituting 10.55/2 for original radius and 7.16/2 for new radius then

\triangle A=\frac {\pi(5.275^{2}-3.58^{2})}{\pi 5.275^{2}}\times 100\approx 53.94

(b)

Similarly, percentage elongation will be found by dividing the change in length by the the original length. In this case, rhe original length was 54.5mm and goes to 69 mm so the change in length is given by subtracting the final length from the original length

Percentage elongation is \frac {69-54.5}{54.5}\times 100\approx 26.61

6 0
4 years ago
A sinusoidal voltage source produces the waveform, v t = 1 + cos 2πft. Design a system with v t as its input such that an LED wi
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Answer:

See explaination

Explanation:

LM358 is the useful IC which works as buffer. It enables circuit to remove overloading effect on each other. Image is in attachment.

We can define a light-emitting diode (LED) as a semiconductor light source that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons

See attached file for detailed solution of the given problem.

3 0
4 years ago
A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB)1 = 6 ft&gt;s. If the attached cord is pulled
Salsk061 [2.6K]

Answer:

r₂ = 1.5 ft

t = 0.75 s

Explanation:

W = 4 lb    ⇒  m = W/g = 4 lb / 32.2 ft/s² = 0.12 slug

v₁ = 6 ft/s

r₁ = 3 ft

v₂ = 12 ft/s

r₂ = ?

t = ?

vr = 2 ft/s

Conserving angular momentum we have:

m*v₁*r₁ = m*v₂*r₂    ⇒     r₂ = v₁*r₁ / v₂

⇒     r₂ = (6 ft/s*3 ft) / (12 ft/s) = 1.5 ft

Now, we get the time as follows:

vr = <em>d</em> / t    ⇒   t = <em>d</em> / vr

where <em>d</em> is

<em>d</em> = Δr = r₁ - r₂ = 3 ft - 1.5 ft = 1.5 ft

finally

t = 1.5 ft / 2 ft/s

⇒ t = 0.75 s

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Pressure stays the same.

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