Question

a coin is tossed two times. the set of outcomes is given as ( s={hh,ht,th,tt} ). let ( x ) represent the number of times heads occurs. complete the table. ( a= ) ( b= ) ( c= )

Explanation:

Step1: Calculate probability for \(X = 0\)

When \(X = 0\) (i.e., \(TT\) outcome). Total outcomes \(n(S)=4\).
Probability \(P(X = 0)=\frac{1}{4}\)

Step2: Calculate probability for \(X = 1\)

When \(X = 1\) (i.e., \(HT\) or \(TH\) outcomes). Number of favorable outcomes \(n = 2\).
Probability \(P(X = 1)=\frac{2}{4}=\frac{1}{2}\)

Step3: Calculate probability for \(X = 2\)

When \(X = 2\) (i.e., \(HH\) outcome). Number of favorable outcomes \(n = 1\).
Probability \(P(X = 2)=\frac{1}{4}\)

Answer:

\(a=\frac{1}{4}\), \(b = \frac{1}{2}\), \(c=\frac{1}{4}\)