"Finding Probability Using Enumeration Method" PPT

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"Finding Probability Using Enumeration Method" PPT

Part One: Basic Knowledge

Question: No matter what event probability we are looking for, we can do a lot of experiments. Finding the frequency to get the probability is universal, but it is really troublesome to find. Is there a simpler way to find the probability of some random events?

1. Pick one randomly from the 5 paper numbers marked 1, 2, 3, 4, and 5 respectively. How many possible numbers are drawn? What is the probability of drawing each number?

2. If you roll a die, how many possible numbers are there on the upward side? What is the probability that the number on the upward side is 1?

Answer: (1) There are 5 possible numbers, and the probability of drawing each number is 1/5.

(2) There are 6 possible points. The probability that the point on the upward side is 1 is 1/6.

Question: What characteristics do the above two experiments have in common?

(1) In a test, there are a limited number of possible results.

(2) In an experiment, various results are equally likely to occur.

Induction: Generally speaking, if there are n possible outcomes in an experiment, and they are all equally likely to occur, and event A contains m of them, then the probability of event A occurring is P(A)=m/ n.

Use enumeration method to find probability PPT, part 2: explanation of examples

[Example 1] Tossing an ordinary cube dice, the probability of the number being 3 is ( )

A.16 B.1/3 C.1/4 D.1/5

[Analysis] The six faces of a cube dice are six integers from 1 to 6. The chances of the six numbers appearing are the same, all 1/6.

[Example 2] Randomly throw a uniform die, the chance that the upward point is a multiple of 2 is ( )

A.1/2 B.2/3 C.3/4 D. 1

[Analysis] The six faces of a cube dice are six integers from 1 to 6. The chances of the six numbers appearing are the same, all 1/6, among which 2, 4, and 6 are all multiples of 2.

Using enumeration method to find probability PPT, part three: selected exercises

1. Xiao Ming called his classmate, but he only remembered 8635*458, and the * digit could not be remembered clearly. If he randomly filled in a number into the * digit, the chance of being able to call through was 1/10.

2. There are 50 students in a class, including 15 students with blood type A, 18 students with blood type B, 14 students with blood type O, and 3 students with blood type AB. Find a student at random. The probability of having type B blood is 9/25.

3. From a deck of 52 playing cards that have been shuffled with the kings and kings removed, the probability of drawing a club is 25%, and the probability of drawing a heart is 25%.

4. From a bag containing 10 white balls, 15 red balls and 25 blue balls, stir it up quickly and take out 1 ball. It is estimated that the chance that it is a white ball is ________, the chance that it is a red ball is _______, and it is blue. The ball's chance is ________.

5. 100 cards (1~100), choose any one from them.

(1) Find the probability that the card taken out is an odd number;

(2) Find the probability that the card taken out is a multiple of 7.

6. Roll a die randomly and calculate the probability of the following events.

(1) The number thrown is divisible by 3; (2) The number thrown is a prime number.

(3) The number thrown is greater than 6; (4) The number thrown is less than 7.

7. As shown in Figure 1, on the circular target, OA=AB=BC=CD=1. If any shot can hit the circular target, which area has the highest probability of landing?

Using enumeration method to find probability PPT, part 4 content: Class summary

In this lesson, we designed two experiments: the lottery experiment and the dice-throwing experiment. Through these two experiments, we can find the following rules: Generally speaking, if in an experiment, there are m possible results, and the probability of their occurrence All are equal, and event A contains n outcomes, then the probability of event A occurring is P(A)=n/m.

Then, we learned two enumeration methods-list method and tree diagram method. In actual question types, we need to choose different methods according to different conditions.

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Update Time: 2024-09-04

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