# Poisson's, Bernoulli's and Laplace's formulas

I'm not sure if i got correct answers as i often choose q and p wrong

1. It is known that a team is equally likely to win three games out of five and two out of four. Find the probability of winning in one game.

My attempt: $$P_5(3)=P_4(2)$$ and using Bernoulli's formula I've got $$10p^3=6p^2$$ and answer p=0,6

1. The probability that the part will not pass the quality test is equal to 0.2. Which the probability that out of 400 randomly selected parts will be defective:

a) 80 parts;

b) from 30 to 80 parts

My attempt: p=0,2 q=0,8 n=400

A)k=80 $$P_{400}(80)=0,05$$ (Laplace's formulas)

B) $$P_{400}(30<=k<=80)=x(0)+x(6,25)=0,5$$

1. The probability of failure for each call is equal to 0.00008. Identify probability that at 1500 calls there will be 6 failures.

My try:

$$P_{1500}(6)=(0,12^6/6!)*exp(-0,12)=3,68*10^{-9}$$

• All I can speak to is your use of Bernoulli's formula, in part 1. I agree with your analysis. By the way: +1 to your query, for good presentation + showing your work. Commented Mar 24, 2021 at 11:41

Given that calculating the exact probability (with the calculator) it is $$\approx 52.987\%$$, using a gaussian approx I get
$$\mathbb{P}(30\leq k\leq 80)=\Phi\left( \frac{80.5-80}{8} \right)-\Phi\left( \frac{29.5-80}{8} \right)\approx 52.492\%$$