Bayesian analysis A certain person buys a houseplant. She buys either a cactus or an orchid. From long experience, I can

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Bayesian analysis
A certain person buys a houseplant. She buys either a cactus or
an orchid. From long experience, I can say that it is a cactus with
a probability of 0.4 or an orchid with a probability of 0.6. She
then goes on holiday and does not water her plants. The plants get
too dry and might die. Under these circumstances, a cactus will die
with a probability of 0.05 and an orchid with a probability of
0.24.
The plant dies.
Apply Bayes’s theorem and show your
working. What is the posterior probability
that it was a cactus?
Excellence question: consider the probability
of the plant being a cactus. Discuss how this probability changes
from prior to posterior in the light of your observation and
whether this is consistent with your intuition.