The document discusses random phenomena and probability. It defines a random phenomenon as one where individual outcomes are uncertain. It provides examples of sample spaces and sample points for events like goals in a game or coin flips. It also includes examples of calculating probabilities of certain outcomes occurring based on the sample space and equally likely outcomes, such as the probability of getting 3 heads in a row or having at least 1 head.

1. 𝒑𝒈 𝟐𝟏𝟏 a phenomenon is said to be random if individual outcomes are uncertain

2. 𝒑𝒈 𝟐𝟏𝟐
sample space
sample point

3. 𝒑𝒈 𝟐𝟏𝟐
1 - goal
0 - no goal
(1, 1)
(1, 0)
(0, 1)
(0, 0)

4. 𝒑𝒈 𝟐𝟏𝟑
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT

5. 𝒑𝒈 𝟐𝟎𝟑
10 𝑠𝑖𝑚𝑖𝑙𝑎𝑟 𝑚𝑎𝑟𝑘𝑒𝑑 𝑏𝑎𝑙𝑙𝑠
𝑐𝑒𝑟𝑡𝑎𝑖𝑛 = < 12 𝑖𝑚𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 = 15

6. 𝒑𝒈 𝟐𝟏𝟒

7. 𝒑𝒈 𝟐𝟏𝟒

8. 𝒑𝒈 𝟐𝟏𝟒

9. 𝒑𝒈 𝟐𝟏𝟒

10. 𝒑𝒈 𝟐𝟏𝟓
=
𝑚
𝑛

11. 𝒑𝒈 𝟐𝟏𝟓
=
𝑚
𝑛

12. 𝒑𝒈 𝟐𝟏𝟖
=
𝑚
𝑛

13. 𝒑𝒈 𝟐𝟏𝟕
=
𝑚
𝑛
𝑃(3) =?
𝑃 (𝑜𝑑𝑑) =?

14. 𝒑𝒈 𝟐𝟏𝟕
=
𝑚
𝑛
𝑃(1𝐻) =?
𝑃 (≥ 1𝐻) =?

15. 𝒑𝒈 𝟐𝟏𝟖
=
𝑚
𝑛
𝑃(2𝐹, 2𝑀) =?

16. 𝒑𝒈 𝟐𝟏𝟖
=
𝑚
𝑛
𝑃(𝑒𝑣𝑒𝑛) =?

17. 𝒑𝒈 𝟐𝟏𝟗
=
𝑚
𝑛

18. 𝒑𝒈 𝟐𝟏𝟗
=
𝑚
𝑛