### Understanding Odds and Probabilities: An Educational Guide#### IntroductionThe chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Conversely, the odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes.#### Example ExplainedFor instance, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or $\frac{2}{3}$.#### Problem StatementA card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a 7 of clubs.```The odds that it is a 7 of clubs are [ ]:[ ].(Simplify your answer)```To solve this, you need to determine the number of successful outcomes (selecting a 7 of clubs) and the number of unsuccessful outcomes (selecting any other card). 1. **Number of Successful Outcomes (Selecting a 7 of Clubs):** There is only 1 such card in a deck.2. **Number of Unsuccessful Outcomes:** There are 51 other cards in a standard deck (52 total - 1 successful outcome = 51).Thus, the odds that it is a 7 of clubs are $1:51$. #### Simplified Answer```The odds that it is a 7 of clubs are [1]:[51].```

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Total number of cards = 52 Number of 7 of clubs = 1 If a random card is selected, the possible…

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The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of 2 successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or . A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a 7 of clubs. The odds that it is a 7 of clubs are :. (Simplify your answer)

The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of 2 successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or . A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a 7 of clubs. The odds that it is a 7 of clubs are :. (Simplify your answer)

MATLAB: An Introduction with Applications

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Publisher:Amos Gilat

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Question

### Understanding Odds and Probabilities: An Educational Guide

#### Introduction
The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Conversely, the odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes.

#### Example Explained
For instance, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or $\frac{2}{3}$.

#### Problem Statement
A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a 7 of clubs.

```
The odds that it is a 7 of clubs are [ ]:[ ].
(Simplify your answer)
```

To solve this, you need to determine the number of successful outcomes (selecting a 7 of clubs) and the number of unsuccessful outcomes (selecting any other card).

1. **Number of Successful Outcomes (Selecting a 7 of Clubs):** There is only 1 such card in a deck.
2. **Number of Unsuccessful Outcomes:** There are 51 other cards in a standard deck (52 total - 1 successful outcome = 51).

Thus, the odds that it is a 7 of clubs are $1:51$.

#### Simplified Answer
```
The odds that it is a 7 of clubs are [1]:[51].
```

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