State with evidence whether each of the following statements...

State, with evidence, whether each of the following statements is true or false: a. The probability of the union of two events cannot be less than the probability of their intersection. b. The probability of the union of two events cannot be more than the sum of their individual probabilities. c. The probability of the intersection of two events cannot be greater than either of their individual probabilities.

Transcript

0:00 Is true.

00:03 First one is true because probability of a union b is equal to p of a intersection b plus b of a complement intersection b plus probability of a intersection b plus probability of a intersection b complement.

00:32 Is the union of 3 mu de x1s, that is a intersection b, a complement intersection b, a intersection b complement.

00:43 Therefore we can write p of a union b is greater than or equal to p of a intersection b.

00:52 This is why this concept is true.

00:55 For the second one, the second one is also true.

00:59 Second one is also true because probability of a union b can be written as p of a plus p of b minus p of a intersection b which is nothing but the addition law of probability addition theorem of probability so this implies p of a union b will be less than or equal to probability of a plus probability of b and the third concept concept is nothing but p of a is equal to p of a intersection b complement plus p of a intersection b which implies which implies p of a intersection b is equal to p of a intersection b is a less than or equal to p of a of b will be equal to p of b intersection a complement plus p of a intersection b.

02:08 Therefore, c is also true.

02:13 While moving on to d, while moving on to d, the d concept is nothing but let a be the event and its complement is a complement.

02:26 Then the probability of the concern event with its corresponding will be equal to 0.

02:33 That is mutually exclusive.

02:37 Mutually exclusive...

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