411 and 413 EXERCISES Introduction se we want to place two b

EXERCISES Introduction se we want to place two balls into two cells 411. Suppose we wantt ) What are the possible outcomes? (b) What are the simple events? in consider Example 4.1.10. Assuming equiprobable property for each of the sample points, 41.2 Again consider Example 4.1.10. A (a) what is the probability of (1, 5)? (b) what is the probability of (1, 6)? In Example 4.1.10, suppose the machine in is to select two digits at random such that the sum of numbers selected is an even. What is the probability that both numbers are even? 413. l4. In Example 4.1.10, suppose that we would let the first digit be an even number. What is the probability that both numbers are even? Consider Exercise 4.1.3. Show that once the machine chooses the first numberat random, the second cannot arbitrarily be chosen. 415 1.6. The probability of an even e probability of an event A and the to probability of its complement A\' always sum D. any positive value A. 0 C. 2 B. 1

Solution

a) first ball in firs cell

second ball in second cell

first ball in second cell

second ball in first cell

both ball in first cell

both ball in second cell

b)

events: select one ball and put it in one cell

4.1.3

we have 9 numbers (from 1 to 9) and they will be even when both will be the same so we only have 9 changes and there are 9C2 = 36 different way to select 2 numbers so

THE PROBABILITY WILL BE = 9/36 = 0.25