The chances of killing a bird are 1 in three attempts. Find the probability that no bird is killed in 3 attempts.

Concept:

Binomial Distribution: 

If ‘n’ and ‘p’ are the parameters, then ‘n’ denotes the total number of times the experiment is conducted and ‘p’ denotes the probability of the happening of the event.

The probability of getting exactly ‘k’ successes in ‘n’ independent trials for a Random Variable X is expressed as P(X = k) and is given by the formula:

P(X = k) = ⁿC_k p^k (1 - p)^{n - k}

Calculation:

The probability that the bird is killed is p = "1 in 3" = \(\frac13\).

∴ The probability that no bird is killed in 3 attempts, will be:

P(X = 0) = 3C0\(\left(\frac13\right)^0\)\(\left(1-\frac13\right)^{3-0}\)

= \(\frac8{27}\).