Question

a coin is tossed 4 times. find the probability that all are tails.
the probability that all are tails is
(type an integer or simplified fraction.)

Explanation:

Step1: Determine probability of single - toss

The probability of getting tails in a single toss of a fair coin is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (tails).

Step2: Use multiplication rule for independent events

Since the coin - tosses are independent events, the probability of getting tails in 4 consecutive tosses is the product of the probabilities of getting tails in each individual toss.
$P(\text{4 tails})=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$

Answer:

$\frac{1}{16}$