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
vagabundo [1.1K]
3 years ago
11

A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a black card and let F be the eve

nt that the card drawn is a 10 card. Find the indicated probability. P(D∪F')
Mathematics
1 answer:
tester [92]3 years ago
3 0

Answer:

The indicated probability of P(D \cup F')=\frac{25}{26}

Step-by-step explanation:

Probability of an event E to be;

P(E) = \frac{Number of events within E}{Total number of possible outcomes}

As per the given condition:

Total number of possible outcomes =  52 cards.

Let the event be D and F as follows;

D : Drawn card is a black card

F : Drawn card is a 10 card.    

Then,

From the given condition:

P(D) = \frac{26}{52}   [Out of 52 cards, 26 were black] ,

P(F) = \frac{4}{52}    [Out of 52 cards, there are four  10 cards]

For any two events A and B we always have;

P(A \cup B) = P(A)+P(B)-P(A \cap B)

Now, we have to find the indicated probability:

P(D \cup F')=P(D)+P(F')-P(D \cap F')               ......[1]

First find the P(F');

P(F') =1-P(F) = 1-\frac{4}{52} =\frac{52-4}{52} =\frac{48}{52}

Also, to find P(D \cap F').

We use the formula :

For any event A and B independent variable.

P(A \cap B) =P(A) \cdot P(B)

then;

P(D \cap F') =P(D) \cdot P(F') = \frac{26}{52} \cdot \frac{48}{52} =\frac{24}{52}

Now, substitute these in [1];

P(D \cup F')=\frac{26}{52} +\frac{48}{52} -\frac{24}{52}=\frac{26+48-24}{52} =\frac{50}{52} = \frac{25}{26}

Therefore, the probability of P(D \cup F')=\frac{25}{26}



You might be interested in
Multiply the following fractions. 5/8 X 7/10 =
patriot [66]

Answer:c

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Due today. Pls help.
alexandr1967 [171]
X is 19
Explanation: because the opposite side of the angle is 134 degrees the other side also has to be 134 degrees. So we do 134-20 which is 114 and then 114 divided by 6 because the number next to x is 6 and the number that is x has to be 19 as 19x6 is 114.
I think this is the right answer and I hope it helps :)
5 0
3 years ago
Read 2 more answers
3x+15=3(x+5) help please?
UkoKoshka [18]
3x+15=3(x+5)

3x+15=3x+15

3x-3x=15-15

Therefore x can be equal to any value.
3 0
2 years ago
Read 2 more answers
News article reports that "Americans have differing views on two potentially inconvenient and invasive practices that airports c
OverLord2011 [107]

Answer:

1) p1=0.83

2) p2=0.81

3) Option B

4) p=0.82

5) s=0.03

6) z=0.67

7) P=0.50

8) Do not reject H0

Step-by-step explanation:

1) The proportion of Republicans who think the full-body scans should be applied in airports is equal to the ratio between the republicans that think it should over the total Republicans in the poll:

p=X/n=258/311=0.83

2) The proportion of Democrats who think the full-body scans should be applied in airports is equal to:

p=X/n=294/363=0.81

3) As we want to know if there is a difference in the proportions calculated, not if one is higher or lower than the other, the correct option is B:

H_0:p_1-p_2=0\\\\H_a:p_1-p_2\neq0

4) The pooled estimate of a proportion is the average of both proportions:

\bar{p}=\frac{p_1+p_2}{2}= \frac{0.83+0.81}{2}=0.82

5) The standard error can be calculated as:

s=\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1} +\frac{\bar{p}(1-\bar{p})}{n_2}} \\\\s=\sqrt{\frac{0.82*0.18}{311} +\frac{0.82*0.18}{363}} \\\\s=\sqrt{0.00047+0.00041} =\sqrt{0.00088}=0.03

6) The z-statistic can be calculated as:

z=\frac{p_1-p_2}{s}=\frac{0.83-0.81}{0.03}=\frac{0.02}{0.03}=0.67

7) The P-value for z=0.67 is P=0.50 (from the standard normal distribution table).

2P(Z>|z|)=0.50286

8) If the significance level is 0.01, the P-value is bigger than the significance level. The effect is not significanct. The null hypothesis is not rejected.

There is not enough evidence to say that both proportions are different.

A. Do not reject H0

8 0
3 years ago
Prove the divisibility:<br><br>45^45·15^15 by 75^30
garri49 [273]

Answer:

3^{75}.

Step-by-step explanation:

We have been an division problem: \frac{45^{45}*15^{15}}{75^{30}}.

We will simplify our division problem using rules of exponents.

Using product rule of exponents (a*b)^n=a^n*b^n we can write:

45^{45}=(9*5)^{45}=9^{45}*5^{45}

15^{15}=(3*5)^{15}=3^{15}*5^{15}

75^{30}=(15*5)^{30}=15^{30}*5^{30}

Substituting these values in our division problem we will get,

\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}

\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}

Using product rule of exponents (a*b)^n=a^n*b^n we will get,

\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}

\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}

\frac{3^{105}*5^{60}}{3^{30}*5^{60}}

\frac{3^{105}}{3^{30}}

Using quotient rule of exponent \frac{a^m}{a^n}=a^{m-n} we will get,

\frac{3^{105}}{3^{30}}=3^{105-30}

3^{105-30}=3^{75}

Therefore, our resulting quotient will be 3^{75}.

7 0
3 years ago
Other questions:
  • Please help me :(
    10·1 answer
  • What would be the solution to 5(g+4)&gt;15? And how would it look like on a number line/graph?
    5·1 answer
  • What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2,
    14·2 answers
  • Please please help, need this done by 1:45!!!!
    5·1 answer
  • The distance between two schools M and K is 2km. A market is situated between M and K . How far is the market from k ?
    8·1 answer
  • Round 18.2 to 1 significant figure
    6·2 answers
  • What is 0.59 in words
    13·2 answers
  • What is the slope and y intercept of the line 6x + 2y = 12
    6·1 answer
  • HELP I HAVE 10 MINUTES PLEASE GIVE ME A REAL ANSWER :
    12·1 answer
  • Alisha earned $12.40 mowing the lawn and $6.50 raking the leaves. How much money did she earn in all?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!