Question

what is the probability to get rain exactly 4 days during a week if probability to get rain in a randomly selected day p 0.4

Answer 1

Task:

What is the probability to get rain exactly 4 days during a week if probability to get rain in a randomly selected day p 0.4

Solution:

Chance of precipitation on any day of the week is always constant. Therefore, we deal with the binomial experiment. Binomial Formula:

$$P _ {n} ^ {k} = C _ {n} ^ {k} p ^ {k} q ^ {n - k}$$

Where $n$ – the number of trials in the binomial experiment,

$k$ – the number of successes that result from the binomial experiment,

$p$ – the probability of success on an individual trial,

$q$ – the probability of failure on an individual trial $(q = 1 - p)$,

$C_n^k$ – the number of combinations of $n$ things, taken $k$ at a time.

$$n = 7$$ $$k = 4$$ $$p = 0.4$$ $$q = 1 - p = 1 - 0.4 = 0.6$$ $$C _ {n} ^ {k} = \frac {n !}{k ! (n - k) !}$$ $$\begin{array}{l} P _ {7} ^ {4} = C _ {7} ^ {4} \cdot 0.4 ^ {4} \cdot 0.6 ^ {7 - 4} = \frac {7 !}{4 ! (7 - 4) !} \cdot 0.4 ^ {4} \cdot 0.6 ^ {3} = \frac {7 \cdot 6 \cdot 5}{3 !} 0.0055296 \\ = 7 \cdot 5 \cdot 0.0055296 = 0.193536 \\ \end{array}$$

Answer: probability to get rain exactly 4 days during a week is 0.193536.