A six-sided die is rolled 30 times. If the die lands with a 1 or 6 facing up, the player wins.If the die lands on 2 , 3 , 4 , 5 the player loses. Consider the table of collected data Number rolled Frequency 1 II 2 IIII 3 IIII I 4 III 5 IIII II 6 IIII III Find the experimental probability of winning and losing.

Total number of outcomes = 30 If the die lands with a 1 or 6 facing up, the player wins.According to the table, 1 have 2 frequency, and 6 have 8 frequency. Therefore, number of favourable cases = 2 + 8 = 10 Experimental Probability of winning = Number of favourable cases total number of outcomes = 10 30 = 1 3 If the die lands on 2 , 3 , 4 or 5 , the player loses. According to the table, 2 , 3 , 4 or 5 have frequency 4 , 6 , 3 or 7 respectively. Therefore, number of favourable cases for losing = 4 + 6 + 3 + 7 = 20 Experimental Probability of losing = 20 30 = 2 3

A six-sided die is rolled 30 times. If the die lands with a 1 or 6 facings up, the player wins. If the die lands on 2 , 3 , 4 or 5 , the player loses. Consider the table of collected data. Number rolled Frequency 1 2 2 4 3 6 4 3 5 7 6 8 What is the theoretical probability of winning? What is the theoretical probability of losing?

Given that, Total number of outcomes = 30 Number of favourable cases for winning = 10 Theoretical Probabilitry = Number of favourable cases Total outcomes Theoretical probability of winning = 10 30 = 1 3 Number of favourable cases of losing = 30 - 10 = 20 Theoretical Probability of losing = 20 30 = 2 3

A six-sided die is rolled 30 times. If the die lands with a 1 or 6 facings up, the player wins. If the die lands on 2 , 3 , 4 or 5 , the player loses. Consider the table of collected data. Number rolled Frequency 1 2 2 4 3 6 4 3 5 7 6 8 Are you surprised by the result of experimental and theoretical probability of winning? Explain.

We know that, Theoretical probability is based on the expected outcomes and experimental probability is based on the series of events of the experiment. Theoretical Probability of winning = 2 6 = 1 3 Experimental probability of winning = 10 30 = 1 3 Yes, we are surprised by the result. Because, Experimental probability and theoretical probability both are same.

A spinner with three equal sections was spun 100 times.The results are as shown: score 1 2 3 frequency 40 35 25 Compare the value to the theoretical probability.

Given that, Total number of outcomes = 100 Number of favourable cases for spinning 3 = 25 from table Experimental probability = Number of favourable cases total number of outcomes = 25 100 = 1 4 = 0 . 25 Total number of sector in figure = 3 Number of favourable case of sector 3 = 1 Theoretical probability = 1 3 = 0 . 333 By comparing experimental and theoretical probability, we have seen that experimental probability is less than theoretical probability.

A spinner with three equal sections was spun 100 times. The results are as shown : Score 1 2 3 Frequency 40 35 25 Find the theoretical and experimental probability of spinning 1 . Represent the experimental probability as a decimal.

Given, total number of outcomes = 3 Number of favourable cases for spinning 1 = 1 Theoretical probability = 1 3 Experimental. Probability: Total number of outcomes = 100 (from table) Number of favourable cases for spinning 1 = 40 Experimental probability = Favourable cases Total outcomes = 40 100 = 0 . 4 Therefore, the theoretical probability and experimental probability of getting 1 are 1 3 and 0 . 4 respectively.

A spinner with three equal sections was spun 100 times. The results are as shown: score 1 2 3 frequency 40 35 25 What would you expect to happen to the experimental probability of spinning 1 if you were to spin the spinner 1000 times or more? Explain.

Experimental probability is the ratio of number of favourable cases to the total number of outcomes. Total number of outcomes = 1000 Experimental Probability of spinning = 40 1000 = 0 . 04 Clearly, if we increase the denominator, experimental probability approaches to closer results. So, we can say that spinning the spinner 1000 or more times will give us closer result.

David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5

Author:David Weber, Talei Kunkel, Alexander Martinez & Rebecca Shultis

David Weber Mathematics Solutions for Exercise - David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5

Attempt the practice questions on Chapter 2: Probability Games and Play, Exercise 22: Practice 5 with hints and solutions to strengthen your understanding. MYP Mathematics A concept-based approach 2 solutions are prepared by Experienced Embibe Experts.

Questions from David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5 with Hints & Solutions

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 4

A six-sided die is rolled $30$ times. If the die lands with a $1$ or $6$ facing up, the player wins.If the die lands on $2, 3, 4, 5$ the player loses. Consider the table of collected data

Number rolled	Frequency
$1$	$II$
$2$	$IIII$
$3$	$IIII I$
$4$	$III$
$5$	$IIII II$
$6$	$IIII III$

Find the experimental probability of winning and losing.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 4

A six-sided die is rolled $30$ times. If the die lands with a $1$ or $6$ facings up, the player wins. If the die lands on $2, 3, 4$ or $5$ , the player loses. Consider the table of collected data.

Number rolled	Frequency
$1$	$2$
$2$	$4$
$3$	$6$
$4$	$3$
$5$	$7$
$6$	$8$

What is the theoretical probability of winning? What is the theoretical probability of losing?

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 4

A six-sided die is rolled $30$ times. If the die lands with a $1$ or $6$ facings up, the player wins. If the die lands on $2$ , $3$ , $4$ or $5$ , the player loses. Consider the table of collected data.

Number rolled	Frequency
$1$	$2$
$2$	$4$
$3$	$6$
$4$	$3$
$5$	$7$
$6$	$8$

Are you surprised by the result of experimental and theoretical probability of winning? Explain.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 5

A spinner with three equal sections was spun $100$ times.The results are as shown:

score	$1$	$2$	$3$
frequency	$40$	$35$	$25$

Question Image

Compare the value to the theoretical probability.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 5

A spinner with three equal sections was spun $100$ times. The results are as shown :

Score	$1$	$2$	$3$
Frequency	$40$	$35$	$25$

Question Image

Find the theoretical and experimental probability of spinning $1$ . Represent the experimental probability as a decimal.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 5

A spinner with three equal sections was spun $100$ times. The results are as shown:

score	$1$	$2$	$3$
frequency	$40$	$35$	$25$

Question Image

What would you expect to happen to the experimental probability of spinning $1$ if you were to spin the spinner $1000$ times or more? Explain.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 6

An $8 ‐$ sided die is rolled, and a coin is tossed. Make a tree diagram of sample space to find the probability of getting a head and an odd number.

EASY

MYP:2

IMPORTANT

MYP Mathematics A concept-based approach 2>Chapter 2 - Probability Games and Play>Practice 5>Q 7

Give an example of a method to simulate the outcomes of choosing one pair of jeans from a group of four pairs which are equally popular.

David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5

David Weber Mathematics Solutions for Exercise - David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5

Questions from David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Probability Games and Play, Exercise 22: Practice 5 with Hints & Solutions

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