f three coins are tossed simultaneously, what is the probability of getting heads on all of them?1/31/41/81/9

1. Break Down the Problem

To find the probability of getting heads on all three coins when tossed simultaneously, we need to determine:

• The total number of possible outcomes when flipping three coins.
• The number of favorable outcomes that result in heads on all three coins.

2. Relevant Concepts

• Each coin has 2 possible outcomes: heads (H) or tails (T).
• The total number of outcomes when flipping $n$ coins is given by $2^n$.

3. Analysis and Detail

1. Total Outcomes: $\text{Total Outcomes} = 2^3 = 8$ The outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

2. Favorable Outcomes: The only favorable outcome for getting heads on all three coins is HHH. Therefore, the number of favorable outcomes is: $\text{Favorable Outcomes} = 1$

3. Probability Calculation: The probability $P$ of getting heads on all three coins is given by the formula: $P(\text{All Heads}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{8}$

4. Verify and Summarize

There is a total of 8 possible outcomes when tossing three coins, and only 1 of those outcomes is favorable (HHH). Thus, the calculated probability is correct.

Final Answer

The probability of getting heads on all three coins is $\frac{1}{8}$.