Three unbiased coins are tossed what is the probability of getting exactly two tails

Three unbiased coins are tossed. What is the probability of getting a at least two head b at most two heads ctwo heads

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Solution : In tossing three coins, the sample space is given gy <br> `S = {"HHH, HHT, HTH, THH, HTT, THT, TTH, TTT"}.` <br> And, therefore, n(S) = 8. <br> (i) Let `E_(1)` = event of getting all heads. Then, <br> `E_(1) = {HHH}` and, therefore, `n(E_(1)) = 1.` <br> `therefore` P (getting all heads) `= P(E_(1)) = (n(E_(1)))/(n(S)) = 1/8.` <br> (ii) Let `E_(2)` = event of getting 2 heads. Then, <br> `E_(2) = {HHT, HTH, THH}` and, therefore, `n(E_(2)) = 3.` <br> `therefore` P (getting 2 heads) `= P(E_(2)) = (n(E_(2)))/(n(S)) = 3/8.` <br> (iii) Let `E_(3)` = event of getting 1 head. Then, <br> `E_(3) = {"HTT, THT, TTH" }` and, therefore, `n(E_(3)) = 3.` <br> `therefore` P (getting 1 head) `= P(E_(3)) = (n(E_(3)))/(n(S)) = 3/8.` <br> (iv) Let `E_(4)` = event of getting at least 1 heads. Then, <br> `E_(4) = {"HTT, THT, TTH, HHT, HTH, THH, HHH"}` and, therefore, `n(E_(4)) = 7.` <br> `therefore` P (getting at least 1 head) `= P(E_(4)) = (n(E_(4)))/(n(S)) = 7/8.` <br> (v) Let `E_(5)` = event of getting at least 2 heads. Then, <br> `E_(5) = {"HHT, HTH, THH, HHH"}` and, therefore, `n(E_(1)) = 1.` <br> `therefore` P (getting all heads) `= P(E_(5)) = (n(E_(5)))/(n(S)) = 4/8 = 1/2.`