1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kryger [21]
3 years ago
6

Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG ind

icate that the first two children born are boys and the third child is a girl, let GBG indicate that the first and third children born are girls and the second is a boy, and so forth. (a) Use set-roster notation to describe the elements in the sample space whose outcomes are all possible genders of the three children. (b) Write each of the following events as a set, in set-roster notation, and find its probability. (i) the event that exactly one child is a girl set probability (ii) the event that at least two children are girls set probability (iii) the event that no child is a girl set probability
Mathematics
1 answer:
Gemiola [76]3 years ago
7 0

Answer:

(a)

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

(b)

i.

1\ girl = \{GBB, BBG, BGB\}

P(1\ girl) = 0.375

ii.

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

P(Atleast\ 2 \ girls) = 0.5

iii.

No\ girl = \{BBB\}

P(No\ girl) = 0.125

Step-by-step explanation:

Given

Children = 3

B = Boys

G = Girls

Solving (a): List all possible elements using set-roster notation.

The possible elements are:

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

And the number of elements are:

n(S) = 8

Solving (bi) Exactly 1 girl

From the list of possible elements, we have:

1\ girl = \{GBB, BBG, BGB\}

And the number of the list is;

n(1\ girl) = 3

The probability is calculated as;

P(1\ girl) = \frac{n(1\ girl)}{n(S)}

P(1\ girl) = \frac{3}{8}

P(1\ girl) = 0.375

Solving (bi) At least 2 are girls

From the list of possible elements, we have:

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

And the number of the list is;

n(Atleast\ 2 \ girls) = 4

The probability is calculated as;

P(Atleast\ 2 \ girls) = \frac{n(Atleast\ 2 \ girls)}{n(S)}

P(Atleast\ 2 \ girls) = \frac{4}{8}

P(Atleast\ 2 \ girls) = 0.5

Solving (biii) No girl

From the list of possible elements, we have:

No\ girl = \{BBB\}

And the number of the list is;

n(No\ girl) = 1

The probability is calculated as;

P(No\ girl) = \frac{n(No\ girl)}{n(S)}

P(No\ girl) = \frac{1}{8}

P(No\ girl) = 0.125

You might be interested in
Simplify 4z2 + z2 + 6a.
podryga [215]
5z^2 + 6a is the simplified expression
5 0
3 years ago
Select from the drop-down menus to correctly complete the statement.
Dominik [7]
We are given the expression
5⁹ x 5³
We can solve this using the rule of exponents which is
a^n x a^m = a^(a + m)
Therefore, the answer is
to keep the base and add the exponents
5⁵⁺³ = 5⁸<span />
4 0
3 years ago
Read 2 more answers
An unfair coin with​ Pr[H] = 0.2 is flipped. If the flip results in a​ head, a marble is selected at random from a urn containin
satela [25.4K]
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2. 
H - head 
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T)   = 0.8
urn
3 red and 5 blue

when heads is obtained 
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12

when tails is obtained 
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3

using bayes rule the answer can be found out, 
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
               = 0.12 / (0.12 + 0.3)
               = 0.12 / 0.42
               = 0.286
the final answer is 0.286
6 0
3 years ago
A multiple choice test consists of eight questions, each of which has five choices. Each question has exactly one correct answer
Nesterboy [21]
I dont under standyou
7 0
3 years ago
Read 2 more answers
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.
jeka57 [31]
x is equal to 5 and y is equal to 29


9 0
3 years ago
Read 2 more answers
Other questions:
  • Use an area model to solve. 1 3/4 X 2 1/2
    13·1 answer
  • The area of a rectangular pool is (14x^2+21x) square feet. If it is 7x feet long, what is the width, in feet?
    12·2 answers
  • Greg received a gift card of $100 for a pizza restaurant. The restaurant charges $15 per pizza. Ashely received gift card of $70
    6·1 answer
  • What is 1.75 divided by 5.25
    10·2 answers
  • Please help!
    15·1 answer
  • Help me on this please
    5·1 answer
  • 20POINTS Given colon g (x) = StartRoot x minus 4 EndRoot and h (x) = 2 x minus 8. What is g(h(10))?
    14·1 answer
  • Determine a series of transformations that would map Figure F onto Figure G.
    5·1 answer
  • The sum of two integers is 250.If one of them is -87,find the others integers​
    10·1 answer
  • The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!