Question

if five coins are flipped, what is the probability of obtaining at least one tail?
p(obtaining at least one tail) = (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the total number of possible outcomes

When flipping a coin, there are 2 possible outcomes (head or tail). When flipping 5 coins, the total number of possible outcomes is \(2\times2\times2\times2\times2 = 2^{5}=32\) (by the multiplication principle).

Step2: Calculate the number of outcomes with no tails (all heads)

There is only 1 outcome with all heads (HHHHH).

Step3: Calculate the probability of the complement event

The probability of getting no tails (all heads) is \(P(\text{no tails})=\frac{1}{32}\).

Step4: Calculate the probability of getting at least one tail

Using the formula \(P(A)=1 - P(\text{complement of }A)\), where \(A\) is the event of getting at least one tail. So \(P(\text{at least one tail})=1 - P(\text{no tails})\).
Substitute \(P(\text{no tails})=\frac{1}{32}\) into the formula: \(P(\text{at least one tail})=1-\frac{1}{32}=\frac{32 - 1}{32}=\frac{31}{32}\)

Answer:

\(\frac{31}{32}\)