one dime is tossed and one die is rolled 120 times. how many times would you expect to toss heads and roll…

Explanation:

Step1: Calculate probability of getting heads

The probability of getting heads when tossing a dime is $P(H)=\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads).

Step2: Calculate probability of rolling an odd - number

A die has 6 possible outcomes ${1,2,3,4,5,6}$, and 3 of them are odd ${1,3,5}$. So the probability of rolling an odd number is $P(O)=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate probability of both events

Since the coin - toss and die - roll are independent events, the probability of getting heads and rolling an odd number is $P = P(H)\times P(O)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step4: Calculate expected number of times

The experiment is repeated $n = 120$ times. The expected number of times of the combined event is $E=n\times P$. Substitute $n = 120$ and $P=\frac{1}{4}$ into the formula, we get $E = 120\times\frac{1}{4}=30$.

Answer:

30