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3 years ago

7

In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of heart

s, queen of spades, and king of clubs). Assuming that aces can be high or low, if you are dealt a five-card hand, what is the probability that it will be a straight with high card 9? (Round your answer to six decimal places.)

1 answer:

GREYUIT [131]3 years ago

5 0

Answer:

$0.000394$

Step-by-step explanation:

First we will find the probability of selecting five cards out of pack of cards

Probability of selecting five cards is equal to

$^{52}C_5$

On expanding we get

$\frac{52!}{47! * 5!} \\$

$\frac{52 * 51 * 50 * 49 * 48 * 47!}{47 ! * 5*4*3*2*1} \\= 2598960$

straight high card $9$ means five cards with values lesser than $9$ but adjacent to it are

$9, 8, 7, 6, 5$

there are four card for each number

Hence, probability of choosing five cards is equal to

$4*4*4*4*4\\= 1024$

Probability of getting a straight with high card 9 is equal to

$\frac{1024}{2598960}$

$0.000394$

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The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 36\degree +70\degree+m$ .

$\Rightarrow 106\degree+m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the two remaining opposite angles of the kite are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

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QUESTION 4

RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.

Using the Pythagoras Theorem, we obtain;

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QUESTION 5

The given figure is an isosceles trapezium.

The base angles of an isosceles trapezium are equal.

Therefore $m$

QUESTION 6

The measure of angle Y and Z are supplementary angles.

The two angles form a pair of co-interior angles of the trapezium.

This implies that;

$m$

$\Rightarrow m$

$\Rightarrow m$

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The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 48\degree +110\degree+m$ .

$\Rightarrow 158\degree+m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the two remaining opposite angles are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

QUESTION 8

The diagonals of the kite meet at right angles.

The length of BC can also be found using Pythagoras Theorem;

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QUESTION 9.

The sum of the interior angles of a trapezium is $360\degree$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

But the measure of angle M and K are congruent.

$\Rightarrow m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

$\Rightarrow m$ .

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