Basics of Probability: Outcomes, Events, and Uniform Probability Model

	Statement (Probability of)
A	Drawing a card with the number $14$ from a standard deck
B	Independence Day will be on July $4^{th}$
C	A coin toss resulting in heads
D	Being born on leap day
E	Getting a number greater than $1$ on the roll of a standard die

Statement (Probability of)

Drawing a card with the number

14

from a standard deck

Independence Day will be on July

4^{th}

A coin toss resulting in heads

Being born on leap day

Getting a number greater than

1

on the roll of a standard die

Drawing a card with the number $14$ from a standard deck

Independence Day will be on July $4^{th}$

A coin toss resulting in heads

Being born on leap day

Getting a number greater than $1$ on the roll of a standard die

	Statement (Probability of)	Likelihood
A	Drawing a card with the number $14$ from a standard deck	Will not happen
B	Independence Day will be on July $4^{th}$	Will happen
C	A coin toss resulting in heads	Equally likely to happen or not happen
D	Being born on leap day	Unlikely to happen
E	Getting a number greater than $1$ on the roll of a standard die	Likely to happen

Statement (Probability of)

Likelihood

Drawing a card with the number

14

from a standard deck

Will not happen

Independence Day will be on July

4^{th}

Will happen

A coin toss resulting in heads

Equally likely to happen or not happen

Being born on leap day

Unlikely to happen

Getting a number greater than

1

on the roll of a standard die

Likely to happen

The probability of each event will be determined by analyzing all possible outcomes and their corresponding favorable outcomes. In addition, given that each experiment follows a uniform probability model, the probability of each outcome occurring is equal.

Picking a Multiple of $4$

This experiment consists of picking a number from the set formed by the numbers from $1$ to $20 .$ The event of interest is that the chosen number corresponds to a multiple of $4 .$ Begin by highlighting the multiples of $4$ from the given set.

Out of the twenty numbers in the set, there are five multiples of

4 .

Therefore, the probability of selecting a multiple of

4

5

out of

20,

which can be expressed as the following ratio.

P (Picking a multiple of 4) = \frac{5}{2 0} ⇕ P (Picking a multiple of 4) = \frac{1}{4}

Drawing a Red Card

A standard deck of cards consists of $52$ cards divided into four suits — spades, clubs, hearts, and diamonds. The colors of the suits are red for hearts and diamonds and black for spades and clubs.

Each suit in a deck of cards contains

13

cards. Since there are two red suits, there are a total of

26

red cards in the deck. Divide

26

by the total number of cards in the deck,

52,

to determine the probability of drawing a red card.

P (Drawing a red card) = \frac{2 6}{5 2} ⇕ P (Drawing a red card) = \frac{1}{2}

Landing on Blue

The roulette wheel is divided into three equal sections representing the different possible outcomes. Of these three outcomes, only one is colored blue, representing the only favorable outcome.

Therefore, the probability of landing on the blue section is given by $\frac{1}{3} .$

Picking the Letter M

For this experiment, a letter will be randomly selected from the English Alphabet. The event is to get the letter M and every letter has an equal chance of being chosen.

Since there are $26$ letters in the alphabet and only one of those is the letter M, the probability of selecting the letter M is $\frac{1}{2 6} .$

Conclusions

All games have been analyzed. The table below pairs each of them with their corresponding probability.

Game (Experiment)	How to Win (Event)	Probability of Winning
Randomly picking a number from the set formed by the numbers from $1$ to $20$	Picking a multiple of $4$	$\frac{1}{4}$
Randomly drawing a card from a standard deck of cards	Drawing a red card	$\frac{1}{2}$
Spinning a $3 -$ colored roulette wheel evenly divided	Landing on blue	$\frac{1}{3}$
Randomly selecting a letter from the English Alphabet	Picking the letter M	$\frac{1}{2 6}$

Out of all the games available, the likelihood of drawing a red card from a standard deck of cards is higher. Therefore, if Davontay and Kevin want to increase their chances of winning, they should choose this game.

$P (Theme Park Passes)$
Experimental Probability	Theoretical Probability
$\frac{3}{2 0} = 0.15$	$\frac{1}{6} = 0.1 \overline{6}$

P (Theme Park Passes)

Experimental Probability

Theoretical Probability

\frac{3}{2 0} = 0.15

\frac{1}{6} = 0.1 \overline{6}

Flipping a Coin and Rolling a Die
Possible Outcomes
$(H, 1)$	$(H, 2)$	$(H, 3)$	$(H, 4)$	$(H, 5)$	$(H, 6)$
$(T, 1)$	$(T, 2)$	$(T, 3)$	$(T, 4)$	$(T, 5)$	$(T, 6)$

Flipping a Coin and Rolling a Die

Possible Outcomes

(H, 1)

(H, 2)

(H, 3)

(H, 4)

(H, 5)

(H, 6)

(T, 1)

(T, 2)

(T, 3)

(T, 4)

(T, 5)

(T, 6)

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Catch-Up and Review

Recording Die Rolls

Probability

Classifying Statements

Hint

Solution

Option A

Option B

Option C

Option D

Option E

Conclusion

Experiment - Probability

Outcome

Event

Burger Restaurant: Hot Wheel and Book Probabilities

Hint

Solution

Complementary Events

The Ball Pit

Hint

Solution

Uniform Probability Model

Spin the Roulette and Win!

Hint