Assuming that the number of accidents that occur in a certain company in a week has a Poisson distribution with a standard deviation of 1.4 . Determine: a) the mean number of accidents that occur in a week b) the probability that in a week, there are no accidents.

(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

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

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

If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card?

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