French Baccalaureat · Mathématiques

Probabilités et géométrie dans l'espace

35 practice questions, each with the answer and an explanation.

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Two independent events $A$ and $B$ have $P (A) = 0.3$ and $P (B) = 0.5$ . What is $P (A \cap B)$ ?
Suppose $P (A) = 0.4$ , $P (B ∣ A) = 0.5$ and $P (B ∣ \overline{A}) = 0.2$ . What is $P (B)$ ?
With the same data, $P (A) = 0.4$ , $P (B ∣ A) = 0.5$ , $P (B ∣ \overline{A}) = 0.2$ and $P (B) = 0.32$ , what is $P (A ∣ B)$ ?
$X$ follows a binomial distribution $B (4, 0.5)$ . What is $P (X = 2)$ ?
$X$ follows $B (10, 0.3)$ . What is the expected value $E (X)$ ?
$X$ follows $B (10, 0.3)$ . What is the variance $V (X)$ ?
A trial succeeds with probability $0.2$ and is repeated $5$ times independently. What is the probability of at least one success?
$X$ follows a normal distribution $N (100, 1 5^{2})$ . What is $P (X \geq 100)$ ?
A bag holds $3$ red and $2$ blue balls. Two balls are drawn without replacement. What is the probability that both are red?
A random variable $X$ takes the values $0$ , $1$ and $2$ with probabilities $0.2$ , $0.5$ and $0.3$ . What is $E (X)$ and what is $V (X)$ ?
In space, what is the distance between $A (1, 2, 3)$ and $B (4, 6, 3)$ ?
What are the coordinates of the vector $A B$ for $A (1, 0, 2)$ and $B (3, 1, 5)$ ?
Let $u (1, 2, 3)$ and $v (2, - 1, 0)$ . What is true about these vectors?
What is an equation of the plane through $A (1, 0, 0)$ with normal vector $n (1, 2, 3)$ ?
What is the distance from $M (1, 1, 1)$ to the plane $x + y + z - 6 = 0$ ?
Which parametric representation describes the line through $A (1, 2, 3)$ with direction vector $u (1, 0, - 1)$ ?
The line $x = 1 + t, y = 2 t, z = 3 - t$ meets the plane $x + y + z = 6$ . At which point?
Are the vectors $u (1, 2, 3)$ and $w (2, 4, 6)$ collinear?
A sphere has the segment $[A B]$ as a diameter, with $A (0, 0, 0)$ and $B (2, 4, 4)$ . What are its center and radius?
How is the orthogonal projection $H$ of a point $M$ onto a plane $P$ characterised?
What is the dot product of $u (- 2; - 2; 3)$ and $v (4; - 3; 3)$ ?
A fair coin is tossed 3 times. What is the probability of exactly 2 heads?
A fair coin is tossed 5 times. What is the probability of exactly 3 heads?
$P (A) = \frac{2}{5}$ , $P (B ∣ A) = \frac{1}{4}$ and $P (B ∣ \overline{A}) = \frac{1}{5}$ . What is $P (B)$ ?
What is the dot product of $u (4; - 2; 0)$ and $v (4; 3; 4)$ ?
A fair coin is tossed 5 times. What is the probability of exactly 1 heads?
What is the dot product of $u (2; 2; 2)$ and $v (2; 1; 0)$ ?
What is the dot product of $u (- 2; 0; 1)$ and $v (- 2; 4; 3)$ ?
$P (A) = \frac{1}{2}$ , $P (B ∣ A) = \frac{1}{4}$ and $P (B ∣ \overline{A}) = \frac{1}{2}$ . What is $P (B)$ ?
$P (A) = \frac{1}{4}$ , $P (B ∣ A) = \frac{1}{2}$ and $P (B ∣ \overline{A}) = \frac{1}{4}$ . What is $P (B)$ ?
$P (A) = \frac{1}{3}$ , $P (B ∣ A) = \frac{3}{4}$ and $P (B ∣ \overline{A}) = \frac{1}{6}$ . What is $P (B)$ ?
What is the dot product of $u (1; - 2; 3)$ and $v (- 1; - 1; 0)$ ?
$P (A) = \frac{1}{5}$ , $P (B ∣ A) = \frac{1}{2}$ and $P (B ∣ \overline{A}) = \frac{1}{10}$ . What is $P (B)$ ?
A fair coin is tossed 4 times. What is the probability of exactly 3 heads?
A fair coin is tossed 6 times. What is the probability of exactly 2 heads?

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