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valina [46]
3 years ago
6

Three cards are randomly selected from a standard 52-card deck, one at a time, with each card re- placed in the deck before the

next one is picked. Find the probability of all three cards are hearts.
Mathematics
1 answer:
hammer [34]3 years ago
3 0

Answer:

\frac{1}{4}

Step-by-step explanation:

Three cards are randomly selected from a standard 52-card deck.

Number of heart cards in a deck = 13

Each card replaced in the deck before the next one is picked.

Probability of first card is heart = P_{1}=\frac{13}{52}

After replacement, the probability of second card is heart = P_{2}=\frac{13}{52}

after replacement, the probability of third card is heart =  P_{3}=\frac{13}{52}

P =  \frac{13}{52} ×  \frac{13}{52} ×  \frac{13}{52}

  =  \frac{39}{156}

  =  \frac{1}{4}

The probability of all three cards are hearts is  \frac{1}{4}

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dezoksy [38]
<span>The urn contains 2 purple balls and 4 white balls. The player pay $4 for start the game and get $1.5 for every ball drawn until one purple ball is drawn. The maximal revenue would be $7.5 when 4 white balls and 1 purple balls are drawn.
If the purple ball is p and white ball is w, t</span>he possible sample space of drawings are {p, wp, wwp, wwwp, wwwwp}

<span>1. Write down the probability distribution for the player earning

The player earning </span>for each event depends on the number of balls drawn subtracted the ticket price.<span>
p= 2/6
The player earnings would be: 1*$1.5 -$4= - $2.5
wp= (4*2)/(6*5) = 4/15
</span>The player earnings would be: 2*1.5- $4= - $1
wwp= (4*3*2)/(6*5*4)= 1/5
The player earnings would be: 3*$1.5 -$4= $0.5
wwwp= (4*3*2*2)/(6*5*4*3*2)= 2/15 
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wwwwp= (4*3*2*2*1)/(6*5*4*3*2*1) = 1/15
The player earnings would be: 5*$1.5 -$4=  $3.5

2. Find its expected value

The expected value would be:
chance of event * earning 
You need to combine the 5 possible outcomes from the number 1 to get the total expected value.

Total expected value= (1/3 * - 2.5)+ (4/15*-1) + (1/5*0.5) + (2/15 *2) + ( 1/15 *3.5)= 
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This game basically a rip off.
6 0
3 years ago
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4 years ago
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natima [27]

Answer:

the answer is 10

Step-by-step explanation:

2x^2-y turns into

2*3^2-8  

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2*9-8

\ /

18-8

 \ /

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5 0
3 years ago
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Nady [450]

Answer:

(2)(18)x

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Step-by-step explanation:

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Answer:

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