7/17/2019 Probability

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CHAPTER 1: PROBABILITY

ASSIGNMENT #1

1. Bill and George go target shooting together. Both shoot at a target at the same time.

Suppose Bill hits the target with probability 0.7, whereas George, independently, hits thetarget with probability 0.4.

(a) Given that ea!tly one shot hit the target, what is the probability that it was

George"s shot#

(b) Given that the target is hit, what is the probability that George hit it#

$. Suppose we have ten !oins whi!h are su!h that i% the ith one is %lipped then heads will

appear with probability i/ 10, i & 1, $, ' 10. hen one o% the !oins is randomly sele!ted

and %lipped, it shows heads. hat is the !onditional probability that it was the %i%th !oin#

. *rn 1 has %ive white and seven bla!+ balls. *rn $ has three white and twelve bla!+ balls.e %lip a %air !oin. % the out!ome is heads, then a ball %rom urn 1 is sele!ted, while i% the

out!ome is tails, then a ball %rom urn $ is sele!ted. Suppose that a white ball is sele!ted.hat is the probability that the !oin landed tails#

4. -hree prisoners are in%ormed by their ailer that one o% them has been !hosen at randomto be ee!uted, and the other two are to be %reed. /risoner A as+s the ailer to tell him

 privately whi!h o% his %ellow prisoners will be set %ree, !laiming that there would be no

harm in divulging this in%ormation, sin!e he already +nows that at least one will go %ree.-he ailer re%uses to answer this uestion, pointing out that i% A +new whi!h o% his %ellows

were to be set %ree, and then his own probability o% being ee!uted would rise %rom 1 to

1$, sin!e he would then be one o% two prisoners. hat do you thin+ o% the ailer"sreasoning#

. 2 gambler has in his po!+et a %air !oin and a two3headed !oin.

(a) e sele!ts one o% the !oins at random, and when he %lips it, it shows heads. hat is

the probability that it is the %air !oin#

(b) Suppose that he %lips the same !oin a se!ond time and again it shows heads. 5ow

what is the probability that it is the %air !oin#

(!) Suppose that he %lips the same !oin a third time and it shows tails. 5ow what is the probability that it is the %air !oin#

PLEASE SHOW YOUR WORK!