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Question 2 (Multiple Choice, Worth 2 Points)

The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

Determine [tex]\(P(\text{at least 2 heads})\)[/tex].

A. 13%
B. 25%
C. 50%
D. 80%



Answer :

GinnyAnswer
Let's solve the problem step-by-step to determine the probability of getting at least 2 heads when tossing a coin 3 times.

### Step 1: Identify the sample space

The sample space for tossing a coin 3 times consists of all possible sequences of heads (H) and tails (T). There are [tex]\(2^3 = 8\)[/tex] possible outcomes, which are:

- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT

### Step 2: Identify the favorable outcomes

We are interested in outcomes with at least 2 heads. Let's list these outcomes and check how many heads each sequence contains:

- HHH (3 heads)
- HHT (2 heads)
- HTH (2 heads)
- THH (2 heads)

These are all the sequences with at least 2 heads.

### Step 3: Count the favorable outcomes

From the list above, we see there are 4 favorable outcomes:
- HHH
- HHT
- HTH
- THH

### Step 4: Calculate the probability

The probability [tex]\(P\)[/tex] of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. So, we have:

[tex]\[ P(\text{at least 2 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{8} = \frac{1}{2} = 0.5 \][/tex]

To express this probability as a percentage, we multiply by 100:

[tex]\[ P(\text{at least 2 heads}) \times 100 = 0.5 \times 100 = 50\% \][/tex]

### Conclusion:

Therefore, the correct answer is 50%.

So, the probability of getting at least 2 heads when tossing a coin 3 times is 50%.

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