b) Passengers arrived randomly at the ABC bus station at a rate of FOUR (4) passengers per hour. Let X be the number of passengers arrived at the ABC bus station. i. Identify the type of probability distribution of \( X \). Find the probability that at most TEN (10) passengers arrived at the ABC bus station during any 60 minutes period of time. Interpret the value. What is the chances (in percentage) that exactly SEVEN (7) passengers arrived iii. at the ABC bus station during any 90 minutes period of time? (3 marks)

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

D. 48 6. Three coins are thrown. What is the chance of throwing 2 heads and a tai in any order?

similarly \( P\left(A / E_{2}\right)=8 / 10 \), and \( P\left(A / E_{3}\right)=4 \) given that the ball drawn is red, what is the third bag by Baye's rule \( =\frac{1}{\frac{1}{3} \times \frac{3}{10}+\frac{1}{3} \times \frac{4}{10}+\frac{1}{3} \times \frac{4}{10}} \) Example 3.12 : Three machines \( E_{1}, E_{2}, E_{3} \) \( 25 \% \), respectively, of the total daily outpl the tubes produced one each of machine those produced on \( E_{3} \) are defective. If on

23. What is the probability that a random arrangement of the letters of the word RESUME has an E on each end? A. 0.067 B. 0.076 C. 0.089 D. 0.095

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