11. Genel toplama kuralına göre; A ve B ayrık veya ayrık olmayan herhangi iki olay olmak üzere, bunlardan en az birinin meydana gelme olasılığı aşağıdakilerden hangisidir? A) \( P(A) \) B) \( P(B) \) C) \( P(A)+P(B) \) D) \( P(A)+P(B)+P(A \cap B) \) E) \( P(A)+P(B)-P(A \cap B) \) A \( B \)

b) Suppose that the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes i. What is the probability that it will take less than two minutes to fill out the form? ii. Determine the cumulative distribution function of the time it takes to fill out the form

Explain how the probability of two independent events occurring together is calculated.

Плотность непрерывной случайной величины равна Плотность \( \mathrm{f}(\mathrm{x})=\left\{\begin{array}{c}c \times \operatorname{arctg} x, \text { при } x \in(0,1) \\ 0, \text { при } x \nexists(0,1)\end{array}\right. \) Найти: С - ?;MX (математическое ожидание) - ?

Найти вероятность попадания случайной величины \( (\mathrm{X}, \mathrm{Y}) \) в квадрат \( \frac{\pi}{6} \leq x \leq \frac{\pi}{2}, \frac{\pi}{6} \leq y \leq \frac{\pi}{2} \) Если известна функция распределения \( \mathrm{F}(\mathrm{x}, \mathrm{y})=\sin x \sin y \) \( \left(0 \leq x \leq \frac{\pi}{2} \quad, 0 \leq y \leq \frac{\pi}{2}\right) \)

3. Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80 . Probability that one of them will be alive next 30 years- \( \begin{array}{ll}\text { (A) } 59 / 9 D & \text { (B) } 44 / 91 \\ \text { (C) } 51 / 91 & \text { (D) } 32 / 91\end{array} \)