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Yakvenalex [24]

2 years ago

6

If you flip a coin 3 times what is the probability of getting at least 2 tails

2 answers:

Softa [21]2 years ago

5 0

$|\Omega|=2^3=8\\ |A|=4\\\\ P(A)=\dfrac{4}{8}=\dfrac{1}{2}=50\%$

elixir [45]2 years ago

4 0

If you flipped a coin 3 times:{

Total number of possible outcomes = 2³ = 8

Total number of outcomes with at least 2 tails = 4
{HTT , THT, TTH, TTT}

P(at least 2 tails ) = 4/8 = 1/2

Answer: 1/2

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Step-by-step explanation:

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Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

a.

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

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$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

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$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

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$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

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Maksim231197 [3]

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