Question

Suppose you toss a coin 4 times what is the probability that you get four tails? Write the probability as a fraction.

Answer 1

Question #39479, Math, Other

Suppose you toss a coin 4 times what is the probability that you get four tails? Write the probability as a fraction.

Solution

We consider a sequence of experiments, each of which results in either a "success" or a "failure". Let $E_{i}, i \geq 1$, denote the event that the $i$-th experiment results in a success. If, for all $i_1, i_2, \ldots, i_n$,

$$P\left(E_{i_1} E_{i_2} \dots E_{i_n}\right) = \prod_{j=1}^{n} P\left(E_{i_j}\right)$$

we say that the sequence of experiments consists of independent trials.

The successive flips of a coin consist of independent trials if we assume (as is usually done) that the outcome on any flip is not influenced by the outcomes on earlier flips. A "success" might consist of the outcome tails and a "failure" heads.

Since $n = 4$, $P(E_i) = 1/2$, for $i = 1, 2, 3, 4$, from the formula (1) we have

$$P\left(E_1 E_2 E_3 E_4\right) = \left(1/2\right)^4 = 1/16.$$

Answer: 1/16