Find the probability that a their sum is even b their

Info iconThis preview shows pages 3–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Find the probability that (a) their sum is even, (b) their product is even. Solution: a) sum is even if “odd-odd-even” or “even-even-even” ( ) 5 . 0 1140 120 10 45 3 20 3 10 1 10 2 10 even is sum = + × = + = P b) product is not even only when all three are odd.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Q. 1 (15 pts) 6 faces of a cubic fair die display the numbers [1], [2,4], [3,4], [4], [5], [6]. The experiment is a single throw of the die. a) Write the sample space of this experiment and assign probabilities to the outcomes in accordance with the axioms. b) Write all events containing a single number. c) P({2}) =? d) Write the smallest field, F , that contains the two arbitrary events E 1 and E 2 of this experiment. e) Write F if E 1 = {4} and E 2 = {(2,4)}; and assign probabilities to its events in accordance with the axioms. Solution : a) = {1,(2,4),(3,4),4 ,5 ,6} P({1}) = P({(2,4)})= P({(3,4)})= P({4})= P({5})= P({6})=1/6 b) {1},{4},{5},{6} c) {2} is not an event d) Smallest field   1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 , , , , , , , , , , , , , E E E E E E E E E E E E E E E E E E E E    e)                         , , 4 , 1, 2,4 , 3,4 ,5,6 , 2,4 , 1, 3,4 ,4,5,6 , 4, 2,4 , 1, 3,4 ,5,6
Background image of page 4
Q.2 (25 pts) A school bus is scheduled to arrive at a bus stop regularly in pre-determined time slots. Unfortunately bus driver may skip the stop (do not stop at the bus stop) with some probability. The probability of the bus stopping at the bus stop is given as p bus . a) Find the probability that there are k stopping buses in n time slots. Anton is a student who decides on his actions based on random events. When a bus stops, Anton flips a coin to decide on getting on the bus or not. Anton boards the bus (gets on the bus) if it is heads. The probability of heads is given as p board . b) Find the probability that Anton boards a bus arriving in the first time slot. c) Find the probability that Anton boards a bus arriving in the second time slot. d) If Anton boards the bus arriving in the 5 th time slot, find the number of ways this event could have happened? e) Find the probability that Anton boards the k th arriving bus on the n th time slot. f) Find the probability that Anton is still at the stop just after ( n-1 ) th time slot. Solution : a) ) 1 ( ; ) ( ) ( } slots time n" " in buses stopping k" {" bus k n k n k p q q p P b) P{Anton boards the first bus} = P{Anton Boards/ Bus Arrives}P{Bus Arrives} = p board p bus . c) In the first time slot, two possible events could have happened: i) Bus does not arrive ii) Bus does arrive, but Anton does not board We show non arriving buses by “-”, Anton not boarding an arriving bus by “x” and Anton boarding the bus by “√”. Then the following could have happened in the first two slots: P(“-“) = q bus P(“x”) =p bus q board ( q board =1-p board ) P(“√”) = p bus p board P{Anton boards the bus in the 2 nd time slot} = (q bus ) (p bus p board ) + (p bus q board ) (p bus p board ) d) Some of the possibilities are: { ----√, x---√, -x--√,--x-√, … , xxxx√ }. The 5 th
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page3 / 15

Find the probability that a their sum is even b their...

This preview shows document pages 3 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online