Question

MHS Student Bookmarks Kami Export - How10.4 ReviewA group of 80 trees in a forest aren't growing properly. A botanist determines:• 68 of the trees have a disease or are being damaged by insects• 54 of the trees have a disease• 30 of the trees are being damaged by insectsWhat is the probability that a randomly selected tree has both a disease and is being damaged by insects?0꾧00 %0o1720ΟΟΟRE10123 9 5

Answer 1

Let the event that a tree has disease be D and the event that tree is being damaged by insects be I.

Therefore,

$\begin{gathered} |D|=54 \\ |I|=30 \\ |D\cup I|=68 \\ \end{gathered}$

Recall that:

$\begin{gathered} |D\cup I|=|D|+|I|-|D\cap I| \\ 68=54+30-|D\cap I| \\ \text{ Therefore,} \\ |D\cap I|=84-68=16 \end{gathered}$

The required probability is given by:

$\frac{|D\cap I|}{80}=\frac{16}{80}=20\%$

Hence, the required probability is 20%=0.2