# 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..???

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 -

1. None of them hit -

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

1. Either of them hit -

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

1. 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.

I assume $A$ and $B$ are people? Let's go with that.

Imagine $A$ throws a stone; either it hits the bird or not. How do you draw the corresponding tree and branches for these two cases? (Probability tree, that is; not the tree with a bird...)

Next, from the two cases of $A$ (i.e., hits the bird or not) you may now consider the two cases of what happens with $B$ throwing their own stone. Similarly, either the stone thrown by $B$ hits or not.

So your possible outcomes are, I think, neither hits the bird, only $A$ hits the bird, only $B$ hits the bird, or both hit the bird. Although, to be realistic, I would think that if the first thrower hits the bird it would alter the probability that the second does, too. (Maybe their throws coincide?) And to be very realistic, probably one should avoid throwing stones at birds (and glass houses) altogether.

• Throwing stones at glass houses is malicious. Throwing stones when you live in a glass house is foolish. I agree that both should be avoided. – Ethan Bolker Dec 26 '16 at 0:04
• @EthanBolker And the same for throwing glass when you live in a stone house! – Benjamin Dickman Dec 26 '16 at 0:05
• Or at stone houses. – Ethan Bolker Dec 26 '16 at 0:09
• @Benjamin, Could you show the.figure please? – pi-π Dec 26 '16 at 0:16
• @user354073 Where is your own attempt? Please insert what you have already tried into your original post; thanks! – Benjamin Dickman Dec 26 '16 at 0:21