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Umnica [9.8K]
3 years ago
7

HELP

Mathematics
1 answer:
pickupchik [31]3 years ago
5 0
C.2/10 inch+ 3/4 inch=R
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A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one
TiliK225 [7]

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are \binom44\binom{48}1=48 possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by \binom{13}1=13. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing \binom41\binom{48}4=778,320 possible hands. Exactly 2 aces are drawn in \binom42\binom{48}3=103,776 hands. And so on. This gives a total of

\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656

possible hands containing at least 1 ace, and hence B occurs with probability

\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. P(A\cap B)=P(A)P(B). This happens if

  • the hand has 4 aces and 1 non-ace, or
  • the hand has a non-ace 4-of-a-kind and 1 ace

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So A\cap B consists of 96 possible hands, which occurs with probability

\dfrac{96}{\binom{52}5}\approx0.0000369

and so the events A and B are NOT independent.

4 0
3 years ago
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mixas84 [53]
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3 years ago
3x-100 what does x equal?
blagie [28]

Answer:

33.333

Step-by-step explanation:

7 0
3 years ago
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!!!!!!!!!HELP ASAP!!!!!!! WORTH 20 POINTS
Juliette [100K]
F(x)=∛x

The domain will be all real numbers.

Answer: A) all real numbers.

Ej: if x=-8 ⇒∛-8=-2

8 0
3 years ago
What is 145 ÷ 891 + 153 ÷ 141 + 1/1?
ruslelena [56]

Answer: Exact form: 94133 / 41877. Mixed number form: 2 10379 / 41877

Step-by-step explanation: divide 145 and 891. Then add 153. Then divide again 141 and 153. Then add 1/1.

Hope this helps!

7 0
3 years ago
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