Math  /  Data & Statistics

QuestionFind the probability that in tossing a fair coin 3 times, there will appear a head at least twice. (Note: write the probability as an integer or as a percentile without the %\% sign)

Studdy Solution

STEP 1

What is this asking? If we flip a fair coin three times, what's the chance we get at least two heads? Watch out! Don't forget to consider *all* the ways we can get at least two heads!

STEP 2

1. List all possible outcomes
2. Identify favorable outcomes
3. Calculate the probability

STEP 3

When we flip a coin three times, we can think of each flip as having two possible outcomes: heads (H) or tails (T).
Let's **systematically list** *all* the possible combinations of heads and tails we can get.

STEP 4

We could get all heads (HHH), or all tails (TTT).
We could get two heads and one tail.
The tail could be the first flip (THH), the second flip (HTH), or the third flip (HHT).
Similarly, we could get two tails and one head: HTT, THT, or TTH.

STEP 5

So, listing them all out, our possible outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
That's a total of 8\boldsymbol{8} possible outcomes!

STEP 6

We're looking for the probability of getting *at least* two heads.
This means we need to count the outcomes with exactly two heads *and* the outcomes with three heads.

STEP 7

Looking back at our list, the outcomes with exactly two heads are: HHT, HTH, and THH.
There's only one outcome with three heads: HHH.

STEP 8

Combining these, our **favorable outcomes** are HHH, HHT, HTH, and THH.
That's a total of 4\boldsymbol{4} favorable outcomes!

STEP 9

The probability of an event is the number of **favorable outcomes** divided by the **total number of possible outcomes**.

STEP 10

We have 4\boldsymbol{4} favorable outcomes (at least two heads) and 8\boldsymbol{8} total possible outcomes.
So, the probability is: Number of favorable outcomesTotal number of possible outcomes=48 \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{8}

STEP 11

We can **simplify** this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4.
This gives us: 48=4÷48÷4=12 \frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}

STEP 12

To express this as a percentage, we multiply by 100: 12100=1002=50 \frac{1}{2} \cdot 100 = \frac{100}{2} = 50 So, the probability is **50**.

STEP 13

The probability of getting at least two heads when flipping a fair coin three times is 50.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord