Question 2

In this hypermarket, a computer model is on promotion. A statistical study made it possible to establish that, each time a customer is interested in this model, the probability that they buy it is equal to 0.3. We consider a random sample of ten customers who were interested in this model. The probability that exactly three of them bought a computer of this model has a value rounded to the nearest thousandth of: a. 0.900 b. 0.092 c. 0.002 d. 0.267

The different sweets in the bags are all coated with a layer of edible wax. This process, which deforms some sweets, is carried out by two machines A and B. When produced by machine A, the probability that a randomly selected sweet is deformed is equal to 0.05.
On a random sample of 50 sweets from machine A, what is the probability, rounded to the nearest hundredth, that at least 2 sweets are deformed?
Answer a: 0.72 Answer b: 0.28 Answer c: 0.54 Answer d: We cannot answer because data is missing

A statistical study established that one in four clients practises surfing.
In a cable car accommodating 80 clients of the resort, the probability rounded to the nearest thousandth that there are exactly 20 clients practising surfing is: a. 0.560 b. 0.25 c. 1 d. 0.103

An urn contains 5 red balls and 3 white balls indistinguishable to the touch.
A ball is drawn from the urn and its colour is noted. This experiment is repeated 4 times, independently, by replacing the ball in the urn each time.
The probability, rounded to the nearest hundredth, of obtaining at least 1 white ball is: Answer A: 0.15 Answer B: 0.63 Answer C: 0.5 Answer D: 0.85

Question 3: In an urn there are 6 black balls and 4 red balls. We perform 10 successive random draws with replacement. What is the probability (to $10^{-4}$ near) of obtaining 4 black balls and 6 red balls?

a. 0.1662

b. 0.4

c. 0.1115

d. 0.8886

An urn contains 10 indistinguishable balls to the touch, of which 7 are blue and the others are green. Three successive draws are made with replacement. The probability of obtaining exactly two green balls is: a. $\left(\frac{7}{10}\right)^2 \times \frac{3}{10}$ b. $\left(\frac{3}{10}\right)^2$ c. $\binom{10}{2}\left(\frac{7}{10}\right)\left(\frac{3}{10}\right)^2$ d. $\binom{3}{2}\left(\frac{7}{10}\right)\left(\frac{3}{10}\right)^2$

We randomly choose, independently, $n$ machines from the company, where $n$ denotes a non-zero natural integer. We assimilate this choice to a sampling with replacement, and we denote by $X$ the random variable that associates to each batch of $n$ machines the number of defective machines in this batch. We admit that $X$ follows the binomial distribution with parameters $n$ and $p = 0.082$.
In this question, we take $n = 50$.
The value of the probability $p(X > 2)$, rounded to the nearest thousandth, is: a. 0.136 b. 0.789 c. 0.864 d. 0.924

We randomly choose, independently, $n$ machines from the company, where $n$ denotes a non-zero natural integer. We assimilate this choice to a sampling with replacement, and we denote by $X$ the random variable that associates to each batch of $n$ machines the number of defective machines in this batch. We admit that $X$ follows the binomial distribution with parameters $n$ and $p = 0.082$.
We consider an integer $n$ for which the probability that all machines in a batch of size $n$ function correctly is greater than 0.4.
The largest possible value for $n$ is equal to: a. 5 b. 6 c. 10 d. 11

On an avenue there are 10 traffic lights. Due to a system failure, the traffic lights were without control for one hour, and fixed their lights only in green or red. The traffic lights operate independently; the probability of showing green is $\frac{2}{3}$ and of showing red is $\frac{1}{3}$. A person walked the entire avenue during the period of the failure, observing the color of the light of each of these traffic lights. What is the probability that this person observed exactly one signal in green?
(A) $\frac{10 \times 2}{3^{10}}$
(B) $\frac{10 \times 2^{9}}{3^{10}}$
(C) $\frac{2^{10}}{3^{100}}$
(D) $\frac{2^{90}}{3^{100}}$
(E) $\frac{2}{3^{10}}$