Tut 1

BM 602 Spring 2009 22-01-2009

Biostatistics Tutorial No. 01 Topics: Sample space, Basic probability.

Note: The term ‘probability’ may be referred to as ‘relative frequency’ or ‘chance of regarding the outcome of interest’. 1. You toss a coin AND roll a die. List the sample space and find the probability of getting a tail and a 4 on the die, assuming the events to be equally likely. 2. There are 4 red balls, 3 white balls and 1 green ball in a box. Give the sample space and calculate the probabilities of a) Picking a red ball. b) Picking a ball that is not white. 3. A game requires you to roll two dice (say red and blue) but then to multiply the numbers on the dice to obtain the score. Enlist the sample space for the above experiment and find the probability of (a) A score greater than 10? (b) A prime number score? (c) The score being a square number? 4. We are playing with a short deck, as shown below.

Let "F" be the event the card drawn is a face card (JQK), "D" be the event the card drawn is a diamond, "A" be the event the card is an ace. a. Find P (F U A) = P (F or A) (i.e. Find the probability the outcome is F or A. ) b. Find P (D ∩ A) = P (D and A) c. Find P (D U A) = P (D or A) d. Are events F and A mutually exclusive? 5. Half the faces of a fair die are painted blue, half yellow. The die is rolled twice. What is the probability the die will turn up blue both times? 6. A fair coin is tossed three times. Give the sample space for the experiment and find the probability of a. getting exactly one head. b. at least one toss being "tail" 7. You play a game in which, to win, you must roll a die and get a 3 or 4, toss a coin and get "tail", and select a card from an ordinary deck and get a red card. Represent the sample space parameterized by general elements and calculate the probability that you will win?

8. A jar contains 100 marbles, identical except that 30 are red, 20 black, 5 green and the rest white. If a marble is taken from the jar at random, what is the probability that the marble is: a. red ? b. black or green? c. not red? d. multicolor?