Respuesta :
Answer:
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 = [tex]\frac{^{13}C_2*^{13}C_3}{^{52}C_5} = 0.0086[/tex] so the third one is not true.
The probability of choosing five spades = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005. The fourth statement is not true
The probability of choosing five clubs = [tex]\frac{^{13}C_5}{^{52}C_5}[/tex] ≈ 0.0005, the fifth one is.
So the answer is the first and fifth statement.
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;
[tex]\displaystyle The \ \mathbf{number} \ of \ \mathbf{possible \ outcomes}} = _{52}C_5 = \frac{52!}{5! \cdot (52 - 5)!} = 2598960[/tex]
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;
[tex]\displaystyle Choosing \ two \ diamonds = _{13}C_2 = \mathbf{\frac{13!}{2! \cdot (13 - 2)!}} = 78[/tex]
The number of ways of choosing three hearts is found as follows;
[tex]\displaystyle Choosing \ three \ hearts = _{13}C_3 = \frac{13!}{3! \cdot (13 - 3)!} = 286[/tex]
The number of ways of choosing two diamonds and three hearts is found as follows;
[tex]\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \frac{_{13}C_2 \times _{13}C_3}{_{52}C_5} = 0.00858[/tex]
Therefore, the number of ways of choosing two diamonds and three hearts ≠ 0.089
[tex]\displaystyle Choosing \ two \ diamonds \ and \ three \ hearts = \mathbf{\frac{_{13}C_2 \times _{13}C_3}{_{52}C_5}} \neq 0.089[/tex]
Fourth statement;
[tex]\displaystyle Probability \ of \ choosing \ five \ spades = \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005[/tex]
Therefore;
[tex]\displaystyle Probability \ of \ choosing \ five \ spades = \mathbf{\frac{_{13}C_5 }{_{52}C_5}} \neq 0.05[/tex]
Fifth statement;
[tex]\displaystyle Probability \ of \ choosing \ five \ clubs= \frac{_{13}C_5 }{_{52}C_5} \approx 0.0005[/tex]
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:
https://brainly.com/question/25718474
