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
cluponka [151]
2 years ago
7

3. Suppose that you draw two cards from a standard 52 card deck. You replace the first card and shuffle thoroughly before you dr

aw the second. [p-4-9-45] a. What is the probability that the first card is 7? b. What is the probability that both cards are 7? c. What is the probability that the first card is not a 7? d. What is the probability that both cards are not 7?
Mathematics
1 answer:
Kruka [31]2 years ago
8 0

Answer:

\text{a)} \frac{1}{17} \text{b)} \frac{1}{221}\text{c)}\frac{12}{13}\text{d)}\frac{188}{221}

Step-by-step explanation:

GIVEN: You draw two cards from a standard 52 card deck. You replace the first card and shuffle thoroughly before you draw the second.

TO FIND: a) What is the probability that the first card is 7 b) What is the probability that both cards are

SOLUTION:

Let \text{A} and \text{B} be two events such that

\text{A}=\text{first card drawn is 7}

\text{B}=\text{Second card is 7}

\text{probability that first card is 7 =P(A)}

<h3> \text{P(A)}=\frac{\text{total 7 numbered cards}}{\text{total cards in deck}}</h3><h3> \text{P(A)}= \frac{4}{52}=\frac{1}{13}</h3>

a)

      \text{probability that first card is 7 =P(A)}

<h3>      \text{P(A)}=\frac{1}{13} </h3>

b)

     \text{probability that both cards are 7}=\text{first card is 7}\times\text{second card is 7}

     \text{probability that both cards are 7}=\text{P(A).P(B)}

     \text{P(B)}=\frac{\text{total number of 7 numbered cards left}}{\text{total number of cards in deck left}}

     \text{P(B)}=\frac{3}{51}=\frac{1}{17}    

     \text{probability that both cards are 7}=\frac{1}{13}\times\frac{1}{17}

     \text{probability that both cards are 7}=\frac{1}{221}

c)

    \text{probability that first card is not 7}=1-\text{probability that first card is 7}

    \text{probability that first card is not 7}=1-\text{P(A)}

    \text{probability that first card is not 7}=1-\frac{1}{13}

    \text{probability that first card is not 7}=\frac{12}{13}

d)

 \text{probability that both cards are not 7}=(\text{first card is not 7}).(\text{second card is not 7})

    \text{probability that both cards are not 7}=\text{[1-P(A)].[1-P(B)]}

    \text{P(B)}=\frac{\text{total 7 numbered cards}}{\text{total cards left in deck}}

    \text{probability that both cards are not 7}=(1-\frac{1}{13})\times(1-\frac{4}{51})

    \text{probability that both cards are not 7}=\frac{12}{13}\times\frac{47}{51}

 

     

You might be interested in
The fraction form of -1.6 is
makkiz [27]

Answer:

-1  2/3

Step-by-step explanation:

8 0
3 years ago
GEOMETRY
NeTakaya

the mall if 4 miles east and 5 miles north, which means that the city's center is 4 miles west and 5 miles south to the mall. Truth is 4 miles west and 2 miles south of the city's  center. This means that:

The mall is 3 miles south of where Truth is (as the west cancel out)

d. 3 miles is your answer

hope this helps

8 0
3 years ago
Find the condition of the expression:√3-2x-x^2
Alex73 [517]

Answer:

-1 <= x <= 1

Step-by-step explanation:

√((1-2x+x^2)+2-2x^2)

= √((1-x)^2 + 2*(1-x)(1+x) )

điều kiện là 1 - x > =0 và 1+x >=0

giải 2 bất phương trình trên ta thu đc kết ququả

7 0
2 years ago
Situation The context you find yourself in is Electronics store owner. The name of your store is Electro Hut. As an owner you wa
denis-greek [22]
It would be 30%profit it in so it would be 3.00
8 0
2 years ago
Assume we need to estimate the mean of a normally-distributed population with great accuracy. Specifically, for significance lev
bulgar [2K]

Answer:

n = 2662.56\sigma^2                                

Step-by-step explanation:

We are given the following in the question:

Significance level = 0.01

Width of interval = 0.1

Population variance = \sigma^2

We have to find the sample size so that the width of the confidence interval is no larger than 0.1

z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58

Formula for sample size:

n = \displaystyle\frac{z^2\sigma^2}{E^2}

where E is the margin of error. Since the confidence interval width is 0.1,

E = 0.05

Putting these values in the equation:

n = \displaystyle\frac{(2.58)^2\sigma^2}{(0.05)^2} = 2662.56\sigma^2

So, the above expression helps us to calculate the sample size so that the width of the confidence interval is no larger than 0.1 for different sample variances.

4 0
3 years ago
Other questions:
  • What is the distance between -6 and 2 on a number line
    9·1 answer
  • A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jacket
    13·2 answers
  • Define the terms factor and quantity. Then for the expression −3(4+x)(z−2−y), list all of the factors, and specify which are qua
    9·1 answer
  • What is the solution to 4log4(x+8)=4^2
    5·2 answers
  • A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain
    5·1 answer
  • What is 52x /1 = 51x/3
    5·1 answer
  • Which one do you like History or Science? I choose history.
    6·2 answers
  • The distance from Rodney's house to the park is 100 meters. If he walks to the park and back to his house, how far will he have
    5·1 answer
  • If F= 1.8C + 32, Solve for C if F = 65​
    5·2 answers
  • Ada and Evie then use an equal number of tickets each. After using up these tickets, they now
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!