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ser-zykov [4K]
3 years ago
13

You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities: a.) The probability th

at a card is a heart, given that it is red? b.) The probability that a card is red, given that it is a heart? c.) Th probability that a card is a king, given that it is red? d.) The probability is a queen, given that it is a face card?
Mathematics
1 answer:
Levart [38]3 years ago
4 0

Answer:

a.) 1/2 or 50%

b.) 1/1 or 100%

c.) 1/13 or 7.69%

d.) 1/3 or 33.33%

Step-by-step explanation:

a.) The probability that a card is a heart, given that it is red?

There are four suits in a deck, two of which are red: hearts and diamonds. Since the number of hearts and diamonds is the same, the probability of the card being a heart, given that it is red is 1/2 or 50%.

b.) The probability that a card is red, given that it is a heart?

All hearts are red cards, therefore, given the card is a heart, there is a 1/1 or 100% probability that it is red.

c.) The probability that a card is a king, given that it is red?

There are 26 red cards, 2 of which are kings. Therefore, the probability of a card being a king, given that it is red is 1/13 or 7.69%.

d.) The probability is a queen, given that it is a face card?

There are 12 face cards in a deck, 4 of which are queens. Therefore, the probability of a card being a queen, given that it is a face card is 4/12 or 1/3 or 33.33%.

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Albert mixes 10 grams of 15% sugar syrup and 25 grams of 10% sugar syrup. C What is the concentration of sugar in the mixture?
ser-zykov [4K]

Answer:

4

Step-by-step explanation:

Given :

10 grams of 15% sugar syrup;

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3 years ago
PLEASE HELP !
rewona [7]
<h3>Answer:  Choice D)  -$22</h3>

You'll lose on average $22 per roll.

====================================================

Explanation:

Normally there is a 1/6 chance to land on any given side of a standard die, but your friend has loaded the die in a way to make it have a 40% chance to land on "1" and an equal chance to land on anything else. Since there's a 40% chance to land on "1", this leaves 100% - 40% = 60% for everything else.  

Let's define two events

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So far we know that P(A) = 0.40 and P(B) = 0.60; I'm using the decimal form of each percentage.

The net value of event A, which I'll denote as V(A), is -100 since you pay $100 when event A occurs. So we'll write V(A) = -100. Also, we know that V(B) = 30 and this value is positive because you receive $30 if event B occurs.

To recap things so far, we have the following:

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  • V(B) = 30

Multiply the corresponding probability and net value items together

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Then add up those products:

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This is the expected value, and it represents the average amount of money you earn for each dice roll. So you'll lose on average about $22. Because the expected value is not zero, this means this game is not mathematically fair.

This does not mean that any single die roll you would lose $22; instead it means that if you played the game say 1000 or 10,000 times, then averaging out the wins and losses will get you close to a loss of $22.

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The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 13 minutes a
Neporo4naja [7]

Answer: I believe the answer is c)-2, 0

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