Mathematics, 24.05.2020 20:58 franstirlacci

A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen, a king, and an ace. The four suits are hearts, diamonds, spades, and clubs. A hand of five cards will be chosen at random. Which statement is true?

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Answer from: kaquino983

The probability of selecting a combination of cards is given by the ratio of

the ways of selecting the cards to the number of possible outcomes.

The true statements are;

The total number possible outcomes is ₅₂C₅.The probability of choosing five clubs is roughly 0.0005.

Reasons:

First statement;

Number of cards in the deck of playing cards = 52

The number of possible outcome is given by the combinations of 5 that can be chosen from 52, as follows;

$\displaystyle The \ \mathbf{number} \ of \ \mathbf{possible \ outcomes}} = _{52}C_5 = \frac{52!}{5! \cdot (52 - 5)!} = 2598960$

Therefore;

The statement; the total number possible outcomes is ₅₂C₅ is true

Third statement;

The number of ways of choosing two diamonds is found as follows;

$\displaystyle Choosing \ two \ diamonds = _{13}C_2 = \mathbf{\frac{13!}{2! \cdot (13 - 2)!}} = 78$

The number of ways of choosing three hearts is found as follows;

$\displaystyle Choosing \ three \ hearts = _{13}C_3 = \frac{13!}{3! \cdot (13 - 3)!} = 286$

The number of ways of choosing two diamonds and three hearts is found as follows;

$\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \frac{_{13}C_2 \times _{13}C_3}{_{52}C_5} = 0.00858$

Therefore, the number of ways of choosing two diamonds and three hearts ≠ 0.089

$\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \mathbf{\frac{_{13}C_2 \times _{13}C_3}{_{52}C_5}} \neq 0.089$

Fourth statement;

$\displaystyle Probability \ of \ choosing \ five \ spades = \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005$

Therefore;

$\displaystyle Probability \ of \ choosing \ five \ spades = \mathbf{\frac{_{13}C_5 }{_{52}C_5}} \neq 0.05$

Fifth statement;

$\displaystyle Probability \ of \ choosing \ five \ clubs= \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005$

Therefore;

The statement, the probability of choosing five clubs is roughly 0.0005 is true.

The possible question options in the question are;

The total possible outcomes is given by ₅₂C₅

The total possible outcomes is given by ₅₂P₅

Probability of choosing 3 hearts and 2 diamonds is 0.089

The likelihood of choosing 5 spades is approximately 0.05

The likelihood of choosing 5 clubs is approximately 0.0005

Learn more about combinations and probability here:

link

Answer from: bobokitty

Step-by-step explanation:

Which statements are true? Check all that apply.

The total possible outcomes can be found using 52C5.

The total possible outcomes can be found using 52P5.

The probability of choosing two diamonds and three hearts is 0.089.

The probability of choosing five spades is roughly 0.05

The probability of choosing five clubs is roughly 0.0005.

Since it can be chosen in any order, we use combination and not permutation. The number of ways of choosing 5 cards from a group of 52 cards is 52C5.

The probability of choosing two diamonds and three hearts = $\frac{^{13}C_2*^{13}C_3}{^{52}C_5} = 0.0086$ so the third one is not true.

The probability of choosing five spades = $\frac{^{13}C_5}{^{52}C_5}$ ≈ 0.0005. The fourth statement is not true

The probability of choosing five clubs = $\frac{^{13}C_5}{^{52}C_5}$ ≈ 0.0005, the fifth one is.

So the answer is the first and fifth statement.

Answer from: Quest

step-by-step explanation: it is d

Answer this multiple choice question correctly for 30 points and

Answer from: Quest

agree

step-by-step explanation:

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