Post History
#2: Post edited
by
tommi
·
2021-07-29T10:58:54Z (over 3 years ago)
- 1. Try with different combinations of probabilities: what is their sum, difference, division. Not all of these are probabilities. (Check this.) This would cause a problem.
- 2. Draw a square; think of it as the unit square $[0, 1] \times [0, 1]$. On $x$-axis mark the (probabilities of) the events $A$ and not $A$. On $y$-axis do the same for $B$ and not $B$. Then try to find $P(A)P(B)$ in the picture; there is a simple geometric interpretation.
Next, try different drawing a similar picture with dependent probabilities. Playing around with ideas can be helpful in clarifying the concepts.
- 1. Try with different combinations of probabilities: what is their sum, difference, division. Not all of these are probabilities. (Check this.) This would cause a problem.
- 2. Draw a square; think of it as the unit square $[0, 1] \times [0, 1]$. On $x$-axis mark the (probabilities of) the events $A$ and not $A$. On $y$-axis do the same for $B$ and not $B$. Then try to find $P(A)P(B)$ in the picture; there is a simple geometric interpretation.
- Next, try drawing a similar picture with dependent probabilities. Playing around with such representations can be helpful in clarifying the concepts.
#1: Initial revision
by
tommi
·
2021-07-29T10:58:03Z (over 3 years ago)
1. Try with different combinations of probabilities: what is their sum, difference, division. Not all of these are probabilities. (Check this.) This would cause a problem. 2. Draw a square; think of it as the unit square $[0, 1] \times [0, 1]$. On $x$-axis mark the (probabilities of) the events $A$ and not $A$. On $y$-axis do the same for $B$ and not $B$. Then try to find $P(A)P(B)$ in the picture; there is a simple geometric interpretation. Next, try different drawing a similar picture with dependent probabilities. Playing around with ideas can be helpful in clarifying the concepts.