A biased coin whose head shows up with probability 0.22, then its tail shows up

ID: 2924009 • Letter: A

Question

A biased coin whose head shows up with probability 0.22, then its tail shows up with probability ____. If this coin is thrown twice, then

There are _____ possible outputs.

There are a total of _____ events, in which there are _____ impossible events, there are _____ certain events, there are _____ possible events.

The probability that the coin disappears is _____

The probability that there are two faces show up is _____

The probability that there are two heads show up is ______

The probability that there are two tails show up is ______

The probability that there is exactly one head shows up is ______

The probability that there are at least one tail show up is _______

The probability that exactly one head shows up given that at least one tail show up is _____

Ans:

Probability of showing up head=p=0.22

Probability of showing up tail=1-p=1-0.22=0.78

if two coins are thrown,then four possible events:

S={HH,HT,TH,HH}

Probbaility of two heads=0.22*0.22=0.0484

Probability of two tails=0.78*0.78=0.6084

Probability of exactly one head shows up=0.22*0.78+0.78*0.22=0.3432

Probability that atleast one tail=1-P(no tail)=1-0.22*0.22=0.9516

Probabilty that exactly one head given that at least one tail=P(exactly one head and atleast one tail)/P(atleast one tail)

As,out of {HT,TH,TT},HT and TH have exactly one head.

P(eaxctly one head/atleast one tail)=0.3432/0.9516=0.3607

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