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Andrew [12]
3 years ago
10

Membership selection. A town council has 10 ​members, 5 Democrats and 5 Republicans. ​(A) If the president and​ vice-president a

re selected at​ random, what is the probability that they are both​ Democrats? ​(B) If a​ 3-person committee is selected at​ random, what is the probability that Republicans make up the​ majority?
Mathematics
1 answer:
SOVA2 [1]3 years ago
7 0

Answer:

(A) P=0.22 or 22% (B) P=50%

Step-by-step explanation:

(A) We have a tree of probabilities, with two steps: president and vice-president.

If the president is elected first, there is a 5/10 chances it will be Democrat.

If this happened, in the election of vice-president, there is 4/9 chances it will be a Democrat chosen again, because there is one Democrat member already selected for President.

So the chances of having a Democrat president and vice president are:

(5/10) x (4/9) = 20/90 = 0.22 = 22%.

(B) We have another tree, with tree steps. The Republicans have majority whenever there are 2 or 3 members in the 3-person comitee.

It can be calculated as the sum of the probability of having 3 republican members (RRR) and the probability of having 2 republican members (RRD, RDR and DRR).

P(RRR) = (5/10) x (4/9) x (3/8) = 1/9

P(RRD) = (5/10) x (4/9) x (5/8) = 1/7

P(RDR) = (5/10) x (5/9) x (4/8) = 1/7

P(DRR) = (5/10) x (5/9) x (4/8) = 1/7

P(RRR) + P(RRD) + P(RDR) + P(DRR) = 1/9 + 1/7 + 1/7 + 1/7 = 1/2 = 50%

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Metal A has a density of 12.7 g/cm3.
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Using the given information, the density of metal B is 8.58 g/cm³

<h3>Calculating density </h3>

From the question, we are to determine the density of metal B

From the given information,

55 g of metal A is combined with metal B to create an alloy with mass 90 g

∴ Mass of metal B in the alloy = 90 g - 55 g = 35 g

Now, we will determine the volume of metal A in the alloy

Using the formula,

Density = Mass / Volume

∴ Volume = Mass / Density

Volume of metal A in the alloy = 55/12.7

Volume of metal A in the alloy = 4.33 cm³

Then, we will determine the volume of the alloy

Volume of the alloy = 90/10.7

Volume of the alloy = 8.41 cm³

∴ Volume of metal B in the alloy = 8.41 cm³- 4.33 cm³

Volume of metal B in the alloy = 4.08 cm³

Now, for the density of metal B

Density = mass / volume

Density of metal B = 35 / 4.08

Density of metal B = 8.58 g/cm³

Hence, the density of metal B is 8.58 g/cm³.

Learn more on Calculating density here: brainly.com/question/13986137

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Solve: <br>x + y = 7<br>3x - 2y = 11<br><br>By using Substituting method.​
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\large\underline{\sf{Solution-}}

\sf  \longmapsto x + y = 7 \: \: - - - (i)

\sf  \longmapsto 3x - 2y = 11 \: \: - - - (ii)

<u>By first equation,</u>

\sf  \longmapsto x + y = 7

\sf  \longmapsto x = 7 - y

<u>Now, we can find the original value of y.</u>

\sf \longmapsto 3x - 2y = 11

\sf  \longmapsto 3(7 - y) - 2y = 11

\sf  \longmapsto 21 - 3y - 2y = 11

\sf  \longmapsto 21 - 5y = 11

\sf  \longmapsto - 5y = 11 - 21

\sf  \longmapsto - 5y =  - 10

\sf  \longmapsto y = \dfrac{ - 10}{ - 5}

\sf  \longmapsto y = 2

<u>Now, we can find the original value of x.</u>

\sf  \longmapsto x + y = 7

\sf  \longmapsto x + 2 = 7

\sf  \longmapsto x = 7 - 2

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