3. If the coca cola drink transporter knows that 25% of the many bottles he is transporting will be found damaged when he reaches his destination. Let X be the number of unloaded bottles at the destination. a)

i) Find the probability that the 8th bottle will be the first one to be found damaged when unloading at the destination.

ii) How many bottles will the transporter expect to unload until the first one is found to be damaged?

b) i) Find the probability that he will have to unload 6 bottles before he finds the damaged one.

ii) How many bottles will the transporter expect to unload before the first one is found to be damaged?

c) i) Find the standard deviation if X will be the number of bottles he will have to unload until he finds the first damaged bottle.

ii) Find the standard deviation if X will be the number of bottles he will have to unload before he finds the first damaged bottle.