Question

A coin is
biased so that a head is twice
as to appear as a trail. If the coin is tossed 6 times find the probabilities of getting
1) exactly a heads
2) atleast 3 heads 3)atmost 4 heads.​

Answer 1

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Step-by-step explanation:

If the coin is biased so that a head is twice as likely to occur as a tail, first you have to figure out the probability for both heads(H) and tails(T). Let’s say that the probability of getting tails is x. Therefore, the probability of getting heads is 2x. So the probability of getting tails out of both possible outcomes is…

p(T|(H∪T))=p(T)/(p(H)+p(T))

=x/(2x+x)

=x/3x

=1/3

Because fractions are being used here and…

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty… ()

The probabilities of all the possible outcomes must add up to 1. The probability of getting heads must therefore be

p(H|(H∪T))=1−p(T)

=1−(1/3)

=2/3

To find the probability of getting 2 tails and 1 heads if the coin is tossed 3 times, it’s necessary to multiply the probabilities.

p(TTH)=p(T)∗p(T)∗p(H)

=(1/3)∗(1/3)∗(2/3)

=2/27

The answer is 2/27.