![andrew763](/avatars/16050.jpg)
andrew763
01.11.2019 •
Mathematics
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. answer all questions.
Solved
Show answers
More tips
- S Sport How to Do Push-ups Correctly?...
- S Style and Beauty How to Grow Hair Faster: Real Methods and Advice...
- F Family and Home How to Remove Fading from Clothes: Tips and Tricks...
- F Food and Cooking How to Make Polendwitsa at Home?...
- F Family and Home Parents or Environment: Who Has the Most Influence on a Child s Upbringing?...
- P Philosophy Unbelievable stories of encounters with otherworldly forces...
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- H Health and Medicine How to Treat Whooping Cough in Children?...
- H Health and Medicine Simple Ways to Lower Cholesterol in the Blood: Tips and Tricks...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
Answers on questions: Mathematics
- M Mathematics I’m literally begging someone please help (just number 10. show work)...
- M Mathematics George is comparing two different phones. The screen of phone A has a width of 5.3 cm. The width of the screen on phone B is 5 and one-third cm. Which statement...
- M Mathematics Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. What type of sampling is used?...
- M Mathematics Simplify the expression 7m+7 -5m...
- M Mathematics Subtract. (8W + 9) - (8W + 3)...
- M Mathematics A rectangular room is 4 times as long as it is wide, and its perimeter is 70 meters. Find the dimension of the room....
- M Mathematics Find the values of y if the distance between the points (–2, 2) and (2, y ) is...
- M Mathematics f(x) = -3x + 4; Find f(2), f(0), and f(-4). (Select all that apply.) f(2)= 10 f(2) = -2 f(0) =4 f(0) = 0 f(-4) = 16 f(-4) = -8...
- M Mathematics XY has a length of 20 and contains a point Z in between. If XZ = -5x+1 and ZY = 3x+5, find ZY....
- M Mathematics Consider the mutations to the appendages and digits. Which mutation would MOST LIKELY result in the extinction of that group of organisms? A) Group A long nails...
Ответ:
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.
1) The probability of having a face card in the first turn
In this case, the chances are 12 in 52:
2) The probability of having a face card in the second turn, having a non-face card in the first turn.
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:
3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.
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:
4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.
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:
With these four probabilities we can calculate the probability of losing this bet:
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:
There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.
Ответ:
the answer to the question would be "b"
"a" would be incorrect because you can turn it into a fraction.
"b" would be incorrect because it forms a perfect square.
"c" would also be incorrect because it forms a perfect a square. 4 x 4 = 16