ISI2016-MMA-11

Question

Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability 4/5 and with water it would die with probability 3/20. The probability that Ravi's neighbor would remember to water the plant is 9/10. If the plant actually died, what is the probability that Ravi's neighbor forgot to water the plant?

• A. 4/5
• B. 27/43
• C. 16/43
• D. 2/25

Answer 1

Ravi's neighbor remember to  water the plant = $\frac{9}{10}$

Ravi's neighbor forgot to  water the plant = $\frac{1}{10}$

With water,

Probability that plant dies = $\frac{3}{20}$

Without water,

Probability that plant dies = $\frac{4}{5}$

the probability that Ravi's neighbor forgot to water the plant if given that plant is actually died is

by bayes' theroem,

= $\frac{\frac{1}{10}*\frac{4}{5}}{(\frac{1}{10}*\frac{4}{5}) + (\frac{9}{10}*\frac{3}{20})} = \frac{\frac{4}{50}}{\frac{4}{50}+\frac{27}{200}} = \frac{\frac{4}{50}}{\frac{43}{200}} = \frac{16}{43}$

Option C.