Chapter 15 Probability

Case Study 1: Tossing a Coin

Case Description:
A teacher decided to demonstrate the concept of probability using a simple experiment: tossing a fair coin. She explained to her students that there are two possible outcomes when a coin is tossed: heads (H) or tails (T). After conducting the experiment 20 times, the results were as follows: heads appeared 12 times, and tails appeared 8 times. The students were asked to calculate the experimental probability of getting heads and tails based on these results.

MCQs:

1. What is the experimental probability of getting heads based on the teacher’s experiment?

   • A) $\frac{2}{5}$
   • B) $\frac{3}{5}$
   • C) $\frac{12}{20}$
   • D) $\frac{4}{5}$

2. What is the experimental probability of getting tails in the experiment?

   • A) $\frac{8}{20}$
   • B) $\frac{2}{5}$
   • C) $\frac{1}{4}$
   • D) $\frac{3}{4}$

3. If the coin is tossed 50 times, how many times would you expect to get heads based on the experimental probability?

   • A) 20
   • B) 25
   • C) 30
   • D) 40

4. Which of the following statements is true based on the results of the experiment?

   • A) The theoretical probability of heads is higher than the experimental probability.
   • B) The experimental probability matches the theoretical probability.
   • C) The experimental probability of tails is less than that of heads.
   • D) The experimental probability of heads is $\frac{1}{2}$.

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Case Study 2: Rolling a Die

Case Description:
In a classroom, a teacher rolled a fair six-sided die 30 times and recorded the outcomes. The results were as follows: 1 appeared 5 times, 2 appeared 6 times, 3 appeared 7 times, 4 appeared 4 times, 5 appeared 5 times, and 6 appeared 3 times. The students were tasked with analyzing the results to determine the experimental probabilities of rolling each number and identifying any trends in the data.

MCQs:

1. What is the experimental probability of rolling a 3?

   • A) $\frac{1}{6}$
   • B) $\frac{7}{30}$
   • C) $\frac{7}{6}$
   • D) $\frac{1}{5}$

2. Which number has the highest experimental probability based on the results?

   • A) 1
   • B) 2
   • C) 3
   • D) 4

3. If the die is rolled 60 times, how many times would you expect to roll a 4 based on the experimental probability?

   • A) 8
   • B) 10
   • C) 12
   • D) 14

4. What is the total number of times all numbers were rolled?

   • A) 30
   • B) 28
   • C) 29
   • D) 31

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Case Study 3: Drawing a Card from a Deck

Case Description:
A group of students conducted an experiment where they drew cards from a standard deck of 52 playing cards without replacement. They drew 20 cards, and the results were: 8 red cards, 6 black cards, 4 face cards. The students needed to calculate the experimental probabilities of drawing a red card, a black card, and a face card from the deck based on this experiment.

MCQs:

1. What is the experimental probability of drawing a red card?

   • A) $\frac{1}{2}$
   • B) $\frac{8}{20}$
   • C) $\frac{4}{10}$
   • D) $\frac{3}{5}$

2. What is the experimental probability of drawing a face card?

   • A) $\frac{1}{5}$
   • B) $\frac{1}{4}$
   • C) $\frac{2}{5}$
   • D) $\frac{4}{20}$

3. If the students were to draw 100 cards, how many red cards would they expect to draw based on the experimental probability?

   • A) 35
   • B) 40
   • C) 50
   • D) 45

4. Which of the following statements about the experiment is correct?

   • A) The total number of cards drawn was less than 20.
   • B) The number of black cards is greater than the number of red cards.
   • C) The experimental probability of a black card is $\frac{6}{20}$.
   • D) Face cards are more than red cards.

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Case Study 4: Weather Forecasting

Case Description:
A meteorologist analyzed the weather forecasts over a month. Out of 30 days, rain was predicted on 10 days and it actually rained on 6 of those days. The students were asked to calculate the probability of the accuracy of the rain forecast based on this data and to determine how this might affect future forecasts.

MCQs:

1. What is the probability of it raining on a day when rain is predicted?

   • A) $\frac{6}{10}$
   • B) $\frac{10}{30}$
   • C) $\frac{3}{5}$
   • D) $\frac{1}{5}$

2. If rain is predicted for the next month, what is the likelihood it will actually rain based on this data?

   • A) 30%
   • B) 50%
   • C) 60%
   • D) 70%

3. How many days did it not rain when it was predicted to rain?

   • A) 4
   • B) 6
   • C) 10
   • D) 20

4. What can be inferred about the reliability of the weather forecast based on the data?

   • A) The forecast is highly reliable.
   • B) The forecast is unreliable.
   • C) There is not enough data to conclude.
   • D) Rain prediction is always accurate.

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Case Study 5: Lottery Draw

Case Description:
A local lottery game involves drawing numbers from a set of 50. Participants select 6 numbers, and if their numbers match the drawn numbers, they win a prize. Last week, a total of 1000 participants entered the lottery. The results showed that 10 players matched all 6 numbers, while 40 matched 5, 100 matched 4, and 200 matched 3. The students need to analyze these results to determine the probability of winning based on different match criteria.

MCQs:

1. What is the probability of matching all 6 numbers?

   • A) $\frac{1}{100}$
   • B) $\frac{1}{1000}$
   • C) $\frac{1}{50}$
   • D) $\frac{10}{1000}$

2. What is the probability of matching 3 numbers?

   • A) $\frac{1}{10}$
   • B) $\frac{2}{5}$
   • C) $\frac{200}{1000}$
   • D) $\frac{3}{10}$

3. How many participants did not match any numbers?

   • A) 650
   • B) 600
   • C) 500
   • D) 700

4. Based on the data, what can be inferred about the lottery game?

   • A) It is easy to win the lottery.
   • B) Very few participants won any prizes.
   • C) Most players matched 5 or more numbers.
   • D) The lottery is rigged.