WEEK 24-EXERCISES-ON-PROBABILITY-TRIALS

Exercises on Probability Trials

Objectives

Start

Coins and Dice

Card Decks

Selecting Balls from a Bag

Other Applications

Summary

Coins and Dice

Let's find out how probable it is to obtain a sum of seven when rolling two dice.

Example 1: When rolling two dice you can obtain a lot of sums like:

🗨️

But only some sums are possible:

Sample space

⚁+⚃=6

Only some 6 sums give 7:

Events

All possibilities

Then:

Launching a Coin and a Die

Example 2: You throw a coin and a die. What's the probability of obtaining a ⚀ and head?

Step 3

Step 1

Step 4

Step 2

|S| =6×2 = 12

p=

1 12

E={(⚀,H)} |E|=1 Just only one case.

Card Decks

Types of Cards in a Deck

Diamonds ♦

Hearts ♥

spades ♠

clubs ♣

🃑 🃒 🃓 🃔 🃕 🃖 🃗 🃘 🃙 🃚 🃛 🃝 🃞

🃁 🃂 🃃 🃄 🃅 🃆 🃇 🃈 🃉 🃊 🃋 🃍 🃎

🂡 🂢 🂣 🂤 🂥 🂦 🂧 🂨 🂩 🂪 🂫 🂭 🂮

🂱 🂲 🂳 🂴 🂵 🂶 🂷 🂸 🂹 🂺 🂻 🂽 🂾

13×4=52 cards

Selecting a Card from a Deck

Example 3: Suppose you have a deck of cards. What is the probability of drawing an Ace

Step 3

Step 1

Step 4

Step 2

|E|=4 There are 4 different aces in a deck.

E={🂡,🂱, 🃁,🃑}

p=

4 52

|S| =13×4 = 52

Selecting Balls from a Bag

Click here to draw >

Selecting a Marble

|S| = 3+4+5 = 12 marbles

|E| = 3 reds

p=

3 12

A bag contains 3 red, 4 blue, and 5 black marbles. What is the probability of picking a red marble?

⬤⬤⬤⬤⬤

⬤⬤⬤

⬤⬤⬤⬤

Solution

Click here to draw >

• p=3/5 Select a ⬤ from {⬤⬤⬤⬤⬤}
• p=1/3 Select a spade from{🂡🂱🃁🂾🃑🂪}
• p=0 Select a ⬤ from {⬤⬤⬤⬤⬤}
• p=1/36 Obtaing ⚂ ⚂ when rolling two dice.

Link the symbols with their meaning

The solution will appear in 30 seconds

p=3/5

Select a ⬤ from {⬤⬤⬤⬤⬤}

Select a ⬤ from {⬤⬤⬤⬤⬤}

p=1/3

Select a spade from{🂡🂱🃁🂾🃑🂪}

p=0

p=1/36

Obtaing ⚂ ⚂ when rolling two dice.

Other Applications

Let's see some examples:

Example 1: Weather forecast says in your neighborhood, there's a 70% chance of rain tomorrow. What does it mean in terms of proportions?

Example 2: A vaccine has a 95% effectiveness rate. What's the probability that the vaccine works? And what is the probability of the vaccine not working?

Working:

p=

95 100

From 100 days with the same weather conditions as tomorrow, 70 were rainy.

q=

5 100

Not working:

Click here to draw >

Sports in a School

|S| = 8 students

B: Basketball player S: Soccer player E={B,B,B,B,S,S,S} |E| = 7

p=

3 12

There are 8 students, 4 basketball players, 3 soccer players and 1 tennis player. Find the probability of selecting one soccer player or one basketball player.

07:00

Summary

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-EXERCISES-ON-PROBABILITY-TRIALS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

Use the probability formula:

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

"MA.8.DP.2 Represent and find probabilities of repeated experiments." MA.8.DP.2.3 Solve real-world problems involving probabilities related to single or repeated experiments, including making predictions based on theoretical probability. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. MA.K12.MTR.6.1 Assess the reasonableness of solutions. ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.

Calculate the size of E

Denoted by |E|

Form the sample space

Think of all possible outcomes or write them (for example, in a tree diagram)

Find Events (E)

From all of the events look up how many satisfy the favorable outcomes.

Verify your results

Probability should always be between 0 and 1.

6x6= 36 possibilities

Find |S|

Calculate the size of sample space.