## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 6 of Exercise 13.1

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##### A coin is tossed three times, where(i) E : head on third toss, F : heads on first two tosses(ii) E : at least two heads, F : at most two heads(iii) E : at most two tails, F : at least one tailDetermine P(E|F)

The sample space of the given experiment will be:

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

(i) Here, E: head on third toss

And F: heads on first two tosses

E = {HHH, HTH, THH, TTH} and F = {HHH, HHT}

E F = {HHH}

So, Now, we know that

By definition of conditional probability,   (ii) Here, E: at least two heads

And F: at most two heads

E = {HHH, HHT, HTH, THH} and F = {HHT, HTH, THH, HTT, THT, TTH, TTT}

E F = {HHT, HTH, THH}

So, Now, we know that

By definition of conditional probability,  (iii) Here, E: at most two tails

And F: at least one tail

E = {HHH, HHT, HTH, THH, HTT, THT, TTH}

And F = {HHT, HTH, THH, HTT, THT, TTH, TTT}

So, Now, we know that

By definition of conditional probability,  6

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