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 \( A B C \) bus station. i. Identify the type of probability distribution of \( X \). (1 mark) ii. 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. (3 marks) T iii. What is the chances (in percentage) that exactly SEVEN (7) passengers arrived at the ABC bus station during any 90 minutes period of time? (3 marks) \( \qquad \) \( \square \) \( \qquad \) \( \qquad \) \( \qquad \)

If you flip a coin and roll a die, what is the probability of getting heads and a 4?

(Bayes' theorem) Example 3.11: Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 re balls respectively. 1 of the bags is selected at random and a ball is draw the ball drawn is red, find the probability that it is drawn from the thirc Sol: Let \( E_{1}, E_{2}, E_{3} \), and A are the events defined as follows. \( E_{1}= \) First bag is chosen \( E_{2}= \) Second bag is chosen \( E_{3}= \) Third bag is chosen \( \mathrm{A}= \) Ball drawn is red Since there are three bags and one of the bags is chosen at random, so \( \mathrm{P}\left(E_{1}\right)=\mathrm{P}\left(E_{2}\right)=\mathrm{P}\left(E_{3}\right)=1 / 3 \) If \( E_{1} \) has already occurred, then first bag has been chosen which conta black balls. The probability of drawing 1 red ball from it is \( 3 / 10 \). So, \( \mathrm{P}( \) 37

The chance of winning a particular lottery game is 1 in 32000, How many tickets would I need to buy in order to improve the chance to 1 in 3200 ? If a machine produces 40 items in 5 minutes, how many liems would it produce in a day?

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

Determina si las siguientes situaciones son eventos dependientes: sacar una bola roja de una caja, no regresarla y luego sacar otra bola.