At a stall in a fun fair, the probability of knocking a coconut off its support is 0.34 - Leaving Cert Mathematics - Question 2(a) - 2021

To find the probability that David knocks the coconut off its support for the first time on his third attempt, we need to consider that he must fail in the first two attempts and then succeed on the third one.

The probability of failing to knock off the coconut is given by:

$P(failure) = 1 - 0.34 = 0.66$

Thus, the probability of failing the first attempt and failing the second attempt, followed by a success on the third attempt is calculated using:

$P(success on 3rd ext{ } attempt) = (0.66)(0.66)(0.34)$

Calculating this gives:

$= 0.66^2 imes 0.34 = 0.4356 imes 0.34 = 0.148104$

Rounded to three decimal places, the answer is 0.148.