Answered: You ask a neighbor to water a sickly…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.7. With water it will die with probability 0.45. You are 84 % certain the neighbor will remember to water the plant.
When you are on vacation, find the probability that the plant will die.
Answer:

You come back from the vacation and the plant is dead. What is the probability the neighbor forgot to water it?

Expert Solution

Step 1

Let A = event that the plant dies

So,

$A \cap B_{1} = e v e n t t h a t i t d i e s a n d w a s n o t g i v e n w a t e r A \cap B_{2} = e v e n t t h a t i t d i e s a n d w a s g i v e n w a t e r B_{1} = e v e n t t h a t w a t e r w a s n o t g i v e n B_{2} = e v e n t t h a t w a t e r w a s g i v e n G i v e n, P (B_{2}) = 0.84 P (B_{1}) = 1 - 0.84 = 0.16 P (\frac{A}{B_{1}}) = 0.7 P (\frac{A}{B_{2}}) = 0.45$

Here, P(A) is to be calculated.

This is done using law of total probability.

$P (A) = {\sum P (A \cap B_{n})}_{n = 1}^{2} = P (A \cap B_{1}) + P (A \cap B_{2}) u \sin g f o r m u l a o f c o n d i t i o n a l p r o b a b i l i t y, = P (\frac{A}{B_{1}}) P (B_{1}) + P (\frac{A}{B_{2}}) P (B_{2}) = 0.7 x 0.16 + 0.45 x 0.84 = 0.49$

Answer:0.49

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