<s>[INST] The probability of hitting a bird with The probability of hitting a bird with a stone lying on a tree by A is $\frac {1}{4}$ and by B is $\frac {3}{5}$. Draw a probability tree diagram to show the probability of all possible ways of hitting the bird.
I couldn't draw the tree diagram. What is the sample space here..???
 [/INST] P(A) = $\frac{1}{4}$
P(A' = Not hitting) = $\frac{3}{4}$
P(B) = $\frac{3}{5}$
P(B' = Not hitting) = $\frac{2}{5}$
There are total three cases -


*

*None of them hit -


P(A') * P(B') =  $\frac{3}{4} \times \frac{2}{5} =  \frac{6}{20}$


*Either of them hit -


P(A) * P(B') + P(A') * P(B) =  $\frac{1}{4} \times  \frac{2}{5} + \frac{3}{4} \times \frac{3}{5} =  \frac{2}{20} + \frac{9}{20} = \frac{11}{20}$


*Both of them hit -


P(A) * P(B) =  $\frac{1}{4} \times \frac{3}{5} =  \frac{3}{20}$
Sample space = $ \left[ \frac{6}{20}, \frac{11}{20}, \frac{3}{20} \right]$
And you can draw Probability Tree Diagram with the help of this link.
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