Find the probability distribution of (i)number of heads in two tosses of a coin (ii)number of tails in the simultaneous tosses of three coins (iii)number of heads in four tosses of a coin

(i) When one coin is tossed twice, the sample space is {HH, HT, TH, TT} Let X represent the number of heads. ∴ X (HH) = 2, X (HT) = 1, X (TH) = 1, X (TT) = 0 Therefore, X can take the value of 0, 1, or 2. It is known that, P (X = 0) = P (TT) P (X = 1) = P (HT) + P (TH) P (X = 2) = P (HH) Thus, the required probability distribution is as follows. X 0 1 2 P (X) (ii) When three coins are tossed simultaneously, the sample space is Let X represent the number of tails. It can be seen that X can take the value of 0, 1, 2, or 3. P (X = 0) = P (HHH) = P (X = 1) = P (HHT) + P (HTH) + P (THH) = P (X = 2) = P (HTT) + P (THT) + P (TTH) = P (X = 3) = P (TTT) = Thus, the probability distribution is as follows. X 0 1 2 3 P (X) (iii) When a coin is tossed four times, the sample space is Let X be the random variable, which represents the number of heads. It can be seen that X can take the value of 0, 1, 2, 3, or 4. P (X = 0) = P (TTTT) = P (X = 1) = P (TTTH) + P (TTHT) + P (THTT) + P (HTTT) = P (X = 2) = P (HHTT) + P (THHT) + P (TTHH) + P (HTTH) + P (HTHT) + P (THTH) = P (X = 3) = P (HHHT) + P (HHTH) + P (HTHH) P (THHH) = P (X = 4) = P (HHHH) = Thus, the probability distribution is as follows. X 0 1 2 3 4 P (X) read less