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babymother [125]
2 years ago
10

Twelve people each have a standard deck of cards. Each person shuffles the deck and draws two cards (without replacement). Anyon

e who draws at least one diamond wins a prize. To the nearest whole number, about how many of the twelve will win a prize? What is the probability that at least one person will win a prize? (Answer correct to four decimal places.) What is the probability that two people will win a prize?
Mathematics
1 answer:
Vlad [161]2 years ago
7 0

Answer:

5

0.9990

0.0401

Step-by-step explanation:

1) Probability(diamond) = 13/52 = 1/4

Probability(not diamond) = 1 - 1/4 = 3/4

Probability of atleast one diamond = 1 - probability of no diamonds

= 1 - (¾ × ¾) = 1 - 9/16 = 7/16

Expected no. = np = 12 × 7/16

= 5.25 = 5 (nearest whole no.)

2) let X be the no. of people winning the prize.

Then X ~ B(12, 7/16)

[ X follows a Binomial Distribution with 12 trials and probability of success (winning prize) = 7/16 ]

P(atleast 1 winning) = 1 - P(X=0)

= 1 - (9/16)^12

= 0.9989966087

= 0.9990 (4 dp)

3) P(X=2) = 12C2 × (7/16)² × (9/16)^10

= 0.0400613268

= 0.0401 (4 dp)

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Answer:

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Step-by-step explanation:

divide the total money by the time to get unit rate such as 4800 divided by 3 equals <u>1600</u>

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6 0
2 years ago
Ten times the sum of half a number and 6 is 8
nexus9112 [7]
Let the required number is 2x ,





According to the condition,



➡ 10 times the sum of half of 2x and 6 = 8

= > 10 \times ( \frac{2x}{2} + 6) = 8 \\ \\ \\ = > 10 \times (x + 6) = 8 \\ \\ \\ = > 10x + 60 = 8 \\ \\ \\ = > 10x = 8 - 60 \\ \\ \\ = > 10x = - 52 \\ \\ \\ = > x = - \frac{ 52}{10} \\ \\ \\ = > x = - 5.2



Therefore the value of x is -5.2


And, required number is -5.2
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3 years ago
For the values a=8 which is a leg of a right triangle and value c=19 which is the hypotenuse find the length of the other leg b
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C^2=a^2+b^2  we are given the hypotenuse of 19 units and one leg of 8 units so:

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361=64+b^2

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