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3 years ago

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Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 4 black balls. Jar 2 has 2 white balls and 1 bla

ck ball. Jar 3 has 2 white balls and 1 black ball. One jar is to be ?selected, and then 1 ball is to be drawn from the selected jar. The probabilities of selecting the? first, second, and third jars are? 1/2?, ?1/3?, and ?1/6 respectively. Find the probability the ball was drawn from Jar 2?, given that the ball is white.

1 answer:

Lady_Fox [76]3 years ago

4 0

Answer:

The probability of finding the white ball from second Jar = 20/39

Step-by-step explanation:

Jar 1 contains 1 White ball and 4 black balls

P(w | J₁) = 1/5

Jar 2 contains 2 White balls and 1 black ball

P(w | J₂) = 2/3

Jar 1 contains 2 White balls and 1 black ball

P(w | J₃) = 2/3

Also, Given

P(J₁) = 1/2

P(J₂) = 1/3

P(J₃) = 1/6

P(w) = P(J₁)×P(w | J₁) + P(J₂)×P(w | J₂) + P(J₃)×P(w | J₃)

P(w) = 1/2×1/5 + 1/3×2/3 + 1/6×2/3 =13/30

To find: P(J₂ | w)

According to conditional probability,

P(J₂ | w) = P(J₂)×P(w | J₂)/P(w)

P(J₂ | w) = (1/3×2/3)/(13/30)

P(J₂ | w) = (1/3×2/3)/(13/30) = 20/39

<u>The probability of finding the white ball from second Jar = 20/39</u>

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3 years ago

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2 years ago

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The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the system. m1 = 4, m2 = 3, m3

viva [34]

Answer:

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Step-by-step explanation:

Center of mass: Center of mass of an object is a point on the object. Center of mass is the average position of the system.

Center of mass of a triangle is the centriod of a triangle.

Given that m₁= 4, m₂=3, m₃=3 and the points are P₁(2,-3), P₂(-3,1) and P₃(3,5)

$M_x$ = ∑(mass × x-co-ordinate)

$M_y$ = ∑(mass × y-co-ordinate)

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The x co-ordinate of the center of mass is the ratio of $M_x$ to the total mass.

The y co-ordinate of the center of mass is the ratio of $M_y$ to the total mass.

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The x co-ordinate of the center of mass is $\frac {8}{10} = \frac {4}{5}$

The y co-ordinate of the center of mass is $\frac{6}{10}=\frac{3}{5}$

Therefore the co-ordinate of the center of mass is = $(\frac{4}{5},\frac{3}{5})$

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