Question

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

Explanation:

Step1: Calculate the total number of possible outcomes

When a coin is flipped, there are 2 possible outcomes (head or tail). When 6 coins are flipped, the total number of possible outcomes is \(2\times2\times2\times2\times2\times2 = 2^{6}=64\) (using the multiplication principle for independent events).

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

The number of outcomes with all tails (no heads) when 6 coins are flipped is 1 (since there is only one way to get all tails: T - T - T - T - T - T).

Step3: Calculate the probability of getting at least one head

The probability of getting at least one head is equal to \(1-\) the probability of getting no heads.
The probability of getting no heads \(P(\text{no heads})=\frac{1}{64}\) (since there is 1 outcome with no heads out of 64 total outcomes).
So \(P(\text{at least one head})=1 - P(\text{no heads})=1-\frac{1}{64}=\frac{64 - 1}{64}=\frac{63}{64}\)

Answer:

\(\frac{63}{64}\)