Question

Three coins are tossed together. Find the probability of getting: (i) exactly two heads (ii) at least two heads (iii) at least one head and one tail (iv) no tails Select the correct answer from above options

Answer 1

(i) Exactly two heads Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH Number of outcomes of exactly two heads are: 3 Probability of getting exactly two heads is = Total numbers/Total number of outcomes = 3/8 ∴ Probability of getting exactly two heads is 3/8 (ii) At least two heads Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH Number of outcomes of at least two heads are: 4 Probability of getting at least two heads is = Total numbers/Total number of outcomes = 4/8 = 1/2 ∴ Probability of getting at least two heads is 1/2 (iii) At least one head and one tail Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH Number of outcomes of at least one head and one tail are: 6 Probability of getting at least one head and one tail is = Total numbers/Total number of outcomes = 6/8 = 3/4 ∴ Probability of getting at least one head and one tail is 3/4 (iv) No tails Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH Number of outcomes of no tails are: 1 Probability of getting no tails is = Total numbers/Total number of outcomes = 1/8 ∴ Probability of getting no tails is 1/8