Are the events
independent?
Yes. The outcome of
rolling one number
cube does not affect
the outcome of rolling
another number cube.
Why are the events
independ ent w hen
you select w ith
replacem ent?
When you replace the
tile, the conditions for
the second selection are
exactly the same as for
the first selection.Suppose you roll a red num ber cube and a blue num ber cube. What is the probability
that you will roll a 3 on the red cube and an even num ber on the blue cube?
P ( r e d 3 ) = g Only one o f the six numbers is a 3.
Q 1
P(blue even) = g = 2 Three °f s'x numbers are even.P(red 3 an d blue even) = P (re d 3) • P ( b l u e e v e n )= g • | = rjL Substitute and then simplify.The probability is -g>.Got It? 2. You roll a red n u m b e r cube an d a blue n u m b e r cube. W hat is th e probability
th a t you roll a 5 on th e red cube an d a 1 or 2 on the blue cube?Fi n d i n g t h e Pr o b a b i l i t y o f I n d ep e n d e n t Ev en t sPr o b l em 3 Se l e ct i n g W i t h R e p l a c e m e n t
Games You choose a tile at random from the game tiles shown.
You replace the first tile and then ch oose again. What is the
probability that you choose a dotted tile and then a dragon tile?
Because you replace th e first tile, the events are in d ep en d en t.
P(dotted) = yg 4 of the 15 tiles are dotted.P(dragon) = yg = g 3^3 1 of the 15 tiles are dragons.P (dragon)15 5
P(dotted and dragon) = P(dotted)= j g • g Substitute.4_
75 Simplify.
The probability th a t you will choose a d otted tile an d th e n a
dragon tile is# Got It? 3. In Problem 3, w hat is th e probability th at you random ly choose a
then, after replacing th e first tile, a flower?bird andTwo events are dependent events if th e occurrence of one event affects th e probability
of th e second event. For example, suppose in Problem 3 th at you do n o t replace the
first tile before choosing another. This changes the set of possible outcom es for your
second selection.778 Ch ap t er 12 Dat a An al ysi s an d Pr o b ab i l i t y