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 = table: coin toss, heads: x (0,1,2), probability: p(x=x) (a, b, c)

Explanation:

Step1: Determine total outcomes

The sample space \(S=\{HH, HT, TH, TT\}\), so there are \(n(S) = 4\) total outcomes.

Step2: Calculate \(a\) (probability of 0 heads)

The outcome with 0 heads is \(TT\). So the number of favorable outcomes \(n = 1\).
Using the probability formula \(P(X = k)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), we get \(a = P(X = 0)=\frac{1}{4}\).

Step3: Calculate \(b\) (probability of 1 head)

The outcomes with 1 head are \(HT\) and \(TH\). So the number of favorable outcomes \(n = 2\).
Using the probability formula, \(b = P(X = 1)=\frac{2}{4}=\frac{1}{2}\).

Step4: Calculate \(c\) (probability of 2 heads)

The outcome with 2 heads is \(HH\). So the number of favorable outcomes \(n = 1\).
Using the probability formula, \(c = P(X = 2)=\frac{1}{4}\).

Answer:

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