4.3 Problems on independence of events  (Page 9/5)

The minterms generated by the class $\{A,B,C\}$ have minterm probabilities

Show that the product rule holds for all three, but the class is not independent.

The class $\{A,B,C,D\}$ is independent, with respective probabilities 0.65, 0.37, 0.48, 0.63. Use the m-function minprob to obtain the minterm probabilities. Usethe m-function minmap to put them in a 4 by 4 table corresponding to the minterm map convention we use.

The minterm probabilities for the software survey in Example 2 from "Minterms" are

Show whether or not the class $\{A,B,C\}$ is independent: (1) by hand calculation, and (2) by use of the m-function imintest.

The minterm probabilities for the computer survey in Example 3 from "Minterms" are

Show whether or not the class $\{A,B,C\}$ is independent: (1) by hand calculation, and (2) by use of the m-function imintest.

Minterm probabilities $p\left(0\right)$ through $p\left(15\right)$ for the class $\{A,B,C,D\}$ are, in order,

$pm=[0.0840.1960.0360.0840.0850.1960.0350.0840.0210.0490.0090.0210.0200.0490.0100.021]$

Use the m-function imintest to show whether or not the class $\{A,B,C,D\}$ is independent.

Minterm probabilities $p\left(0\right)$ through $p\left(15\right)$ for the opinion survey in Example 4 from "Minterms" are

$pm=[0.0850.1950.0350.0850.0800.2000.0350.0850.0200.0500.0100.0200.0200.0500.0150.015]$

Show whether or not the class $\{A,B,C,D\}$ is independent.

The class $\{A,B,C\}$ is independent, with $P\left(A\right)=0.30$ , $P\left(B^{c}C\right)=0.32$ , and $P\left(AC\right)=0.12$ . Determine the minterm probabilities.

The class $\{A,B,C\}$ is independent, with $P(A\cup B)=0.6$ , $P(A\cup C)=0.7$ , and $P\left(C\right)=0.4$ . Determine the probability of each minterm.