First slide

Theorems of probability

Question

$Let E^{C} denote the complement of an event E . Let E, F, G$ $be pairwise independent events with P (G) > 0 and P (E \cap F \cap G) = 0 .$
$Then P (E^{C} \cap F^{C} / G) equals$

Moderate

A

$P (E^{C}) + P (F^{C})$
B

$P (E^{C}) - P (F^{C})$
C

$P (E^{C}) - P (F)$
D

$P (E) - P (F^{C})$

Solution

We have,
$\begin{array}{l} E \cap F \cap G = ϕ \\ P (E^{c} \cap F^{c} / G) \\ = \frac{P (E^{c} \cap F^{c} \cap G)}{P (G)} \\ = \frac{P (G) - P (E \cap G) - P (G \cap F)}{P (G)} \end{array}$
$[From Venn diagram E^{c} \cap F^{c} \cap G = G - E \cap G - F \cap G]$
$= \frac{P (G) - P (E) P (G) - P (G) P (F)}{P (G)}$ ["' E' F' G are pairwise independent]
$= 1 - P (E) - P (F) = P (E^{c}) - P (F)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App