a fair coin is tossed three times in succession. the sample space is shown, where h represents a head and t…

a fair coin is tossed three times in succession. the sample space is shown, where h represents a head and t represents a tail. find the probability of getting exactly zero tails.\nthe probability of getting exactly zero tails is \n(simplify your answer.)

a fair coin is tossed three times in succession. the sample space is shown, where h represents a head and t represents a tail. find the probability of getting exactly zero tails.\nthe probability of getting exactly zero tails is \n(simplify your answer.)

Answer

Explanation:

Step1: Determine total number of outcomes

The sample - space has 8 elements, so the total number of outcomes $n(S)=8$.

Step2: Determine number of favorable outcomes

Getting exactly zero tails means getting all heads, and there is only 1 outcome of getting all heads, i.e., (H,H,H), so the number of favorable outcomes $n(E) = 1$.

Step3: Calculate probability

The probability formula is $P(E)=\frac{n(E)}{n(S)}$. Substituting $n(E) = 1$ and $n(S)=8$, we get $P(E)=\frac{1}{8}$.

Answer:

$\frac{1}{8}$