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
mezya [45]
3 years ago
15

Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least

one of the four is a face card (i.e., Jack, Queen, or King). Should you take the bet? Why? (Hint: See how the probability of this event compares to 50%. If this is too hard, try it with replacement first.) (b) What if the bet involves picking three cards at random instead of four? Should you take the bet then? Why? (c) Refer to the posted Rcode folder for this part. Please answer all questions.
Mathematics
1 answer:
Tatiana [17]3 years ago
5 0

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

<u><em>1) The probability of having a face card in the first turn</em></u>

In this case, the chances are 12 in 52:

P_1=P(face\, card)=12/52=0.231

<u><em>2) The probability of having a face card in the second turn, having a non-face card in the first turn.</em></u>

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181

<u><em>3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.</em></u>

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141

<u><em>4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.</em></u>

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

P_4=(40/52)*(39/51)*(38/50)*(12/49)\\\\P_4=0.769*0.765*0.76*0.245=0.109

With these four probabilities we can calculate the probability of losing this bet:

P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662

The probability of losing is 66.2%, which is the same as saying you have (1-0.662)=0.338 or 33.8% of winning chances. Losing is more probable than winning, so you should not take the bet.

b) If the bet involves 3 cards, the only difference with a) is that there is no probability of getting the face card in the fourth turn.

We can calculate the probability of losing as the sum of the first probabilities already calculated:

P=P_1+P_2+P_3=0.231+0.181+0.141=0.553

There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.

You might be interested in
Jared‘s grandmother gave him $19 for his birthday he brought eight dollars worth of candy and spent another four dollars on a ne
cestrela7 [59]

Answer:

$7

Step-by-step explanation:

To solve this one we will subtract how much he spends from what he has.  At the start he had 19 and then spent 8 meaning he now has 8 less than when we started so 19-8 is 11.  He now as 11 dollars, then he spend another 4 meaning we have to subtract another 4 dollars.  11-4 is 7.  So he as 7 dollars left at the end.

I hope this helps and please don't hesitate to ask if there is anything still unclear!

7 0
3 years ago
Read 2 more answers
Each week our school’s team travels to other schools for competitions. Today the five members of the gymnastics team and seven w
Aliun [14]

Answer: The answer is 9.


Step-by-step explanation:  Given that five members of gymnastics team and 7 members of weight lifting team are travelling in two vans  to the rival school for competition. We are to find the number of ways in which they can ride in two vans such that no van contains more than eight passengers and there is at least one member of each team in each van.

Let 'g' and 'w' denote a member of gymnastics team and weight lifting team respectively.

Then, the possibilities are

For 1 g, we can choose 3w, 4w, 5w, 6w.

For 2g, we can choose 2w, 3w, 4w, 5w, 6w.

For 3g, we can choose 1w, 2w, 3w, 4w, 5w.

For 4g, we can choose, 1w, 2w, 3w, 4w.

Therefore, there are (4 + 5 + 5 + 4) = 18 ways.

Since, here the position of the vans does not matter, so the options are double here. Hence, we must divide it by 2.

Thus, the total number of ways = 9.


4 0
3 years ago
What is the range of the function f(x) = -2(6^x) +3?<br><br><br> Answer is B
Oksana_A [137]

Answer:

You are right

Step-by-step explanation:

5 0
3 years ago
What quantum numbers specify these subshells 5s 2p 3d?
Ivan
5s subshell represent that n is equal to 5 and l is equal to 0.
2p subshell represent that n is equal to 2 and l is equal to 1.
3d subshell represent that n is equal to 3 and l is equal to 2.
The numbers gives us the value of n and the letter gives us the value of l.
s means l = 0 
p means l = 1 
d means l = 2
f means l = 3 
5 0
3 years ago
What does -3x + 7 + -6x t 9 equal
liberstina [14]

Answer:

-50x

Step-by-step explanation:

-6x times 9 which is -54x

-54x-3x = -57x

-54x+7

8 0
3 years ago
Other questions:
  • PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inher
    7·1 answer
  • Simplify 7.5 + n + 9.63. <br> 7.5n + 9.63<br> 17.13n <br> n + 17.13
    10·2 answers
  • What is the volume of 22.5 g of metal with a density of 2.81 g/cm
    11·1 answer
  • Plz help math
    7·2 answers
  • The area of triangle formed by points of intersection of parabola y=a(x−1)(x−4) with the coordinate axes is 3. Find a if it is k
    11·1 answer
  • Jackie earned $15 babysitting. she went to the movies the next night and spend $10. her brother paid her back $4 the next day sh
    5·1 answer
  • Robert's monthly bank statement showed the following deposits and withdrawals: -−$113.24, $98.07, -−$18.74, -−$98.17, $37.13 If
    15·1 answer
  • 24 N of force is applied to stop a 12 kg bowling ball. What is the acceleration on the ball?
    6·1 answer
  • I need help with school
    11·1 answer
  • How to write equation of line
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!