Question

if you roll a fair six - sided die, what is the probability of rolling a 2 or a 5?
options: 2/3, 1/2, 1/3, 1/6
question 19
if you flip a coin and then roll a six - sided die, how many possible outcomes are there in total?
options: 12, 6, 8, 4

Explanation:

First Question (Probability of rolling a 2 or 5 on a die)

Step1: Identify total and favorable outcomes

A fair six - sided die has 6 possible outcomes ($1,2,3,4,5,6$). The favorable outcomes (rolling a 2 or a 5) are 2.

Step2: Apply probability formula

The probability $P$ of an event is given by $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P = \frac{2}{6}=\frac{1}{3}$.

Step1: Outcomes of coin flip

A coin flip has 2 possible outcomes (heads or tails).

Step2: Outcomes of die roll

A six - sided die has 6 possible outcomes.

Step3: Apply multiplication principle

For two independent events, the total number of outcomes is the product of the number of outcomes of each event. So total outcomes $= 2\times6 = 12$.

Answer:

1/3

Second Question (Total outcomes of coin flip and die roll)