Probability of all men rescue from gun shot!

Question

Suppose a gun have 3 bullet in it, out of 6 bullet spaces.

There are 3 men front of gun man.

Now gun man roll gun bullet randomly and start shoot 3 men (shot 3 times at different person).

=> What is probability of all men save ?

=> What is probability of all men shot ?

=> What is probability of at least one man shot ?

=> What is probability of at least one man save ?

Do we need to consider this event as Dependent ?

[ Event is considered from popular bollywood film Sholey ]

Sholey movie scene

.. had calculated all men saved probability as below, not sure is it correct or not,

All man saved = 1 - (1/2 + 1/2 + 1/2) ~ 0.125

UPDATE: Not sure why some people giving down vote, any way I don't care, I got answer from @trueblueanil :D :D

Answer 1

For all men saved, your computation is obviously incorrect as it will yield a negative probability.

• It is the multiplication law, not the addition law that is needed
• As shots are fired, the probabilities will go on changing depending on what has happened earlier (dependent)

For all men saved, $Pr = \frac36\cdot\frac25\cdot\frac14 = \frac1{20} = 5$ %

Seemingly oddly, probability of all men being shot is also the same !

You can try your hand at the other cases