Question

DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: An odd number on each of the last two rolls Event B: An even number on the last roll Event C: An even number on the last roll or the second roll (or both) Explanation Check 000 0 0 OOE EEE O Outcomes OEO 0 0 EOO EEO EOE OEE 0 0 Probability 0 0 0 00 음 0/5 X Nikida V Españe

Answer 1

Event A:

The event A occurs when an odd number is rolled in the second roll and in the third roll. We can see in the table that the outcomes that correspond with this event are:

OOO

EOO

Now to calculate the probability, we need to divide the number of favorable outcomes by the number of total outcomes. There are 8 possible outcomes, and the favorable outcomes for event A are 2. Thus:

`P(A)=(2)/(8)=(1)/(4)`

Event B:

In event B we want the last roll to be even. Then, the outcomes corresponding to this event are:

OOE

EEE

EOE

OEE

The number of favorable outcomes is 4, the total outcome is 4:

`P(B)=(4)/(8)=(1)/(2)`

Event C:

Here, we are looking for outcomes with an even number in the second or last roll (or both). Thus the outcomes that satisfy this are:

OOE

EEE

OEO

EEO

EOE

OEE

The number of favorable outcomes is 6, and the number of total outcomes is 8:

`P(C)=(6)/(8)=(3)/(4)`