We read your photo as:

A fair coin is tossed twice. Find the probability that: a) 2 heads appear, b) 2 tails appear, c) at least one head appears.

Mathematics

ScanSolve AI Answer

Answers

3 parts
a

14\frac{1}{4}

b

14\frac{1}{4}

c

34\frac{3}{4}

Step-by-step solution

6 steps

When a fair coin is tossed twice, the total possible outcomes are:
HH (Head, Head)
HT (Head, Tail)
TH (Tail, Head)
TT (Tail, Tail)
There are 4 total possible outcomes.

Part a· 2 steps

Find the probability that 2 heads appear.

  1. Identify the favorable outcome.

    The outcome where 2 heads appear is HH.

  2. Calculate the probability.

    There is 1 favorable outcome out of 4 total outcomes.

    P(2 heads)=Number of favorable outcomesTotal number of possible outcomes=14P(\text{2 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{4}

    The probability that 2 heads appear is 14\boxed{\frac{1}{4}}.

Part b

14\frac{1}{4}

Find the probability that 2 tails appear.

  1. Identify the favorable outcome.

    The outcome where 2 tails appear is TT.

  2. Calculate the probability.

    There is 1 favorable outcome out of 4 total outcomes.

    P(2 tails)=Number of favorable outcomesTotal number of possible outcomes=14P(\text{2 tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{4}

    The probability that 2 tails appear is 14\boxed{\frac{1}{4}}.

Part c

34\frac{3}{4}

Find the probability that at least one head appears.

  1. Identify the favorable outcomes.

    "At least one head" means one head or two heads. The outcomes are HH, HT, TH.

  2. Calculate the probability.

    There are 3 favorable outcomes out of 4 total outcomes.

    P(at least one head)=Number of favorable outcomesTotal number of possible outcomes=34P(\text{at least one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{4}

    The probability that at least one head appears is 34\boxed{\frac{3}{4}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA fair coin is tossed 3 times, what is the probability of getting at least two heads?QIf two fair coins are tossed, what is the probability of getting at least one head?QA coin is tossed thrice. i) Find the probability that there are two heads given that at least one is…QA coin is tossed twice, find the probability of getting no tails.QA coin tossed three times, find the probability of getting: (i) 3 heads (ii) Not 3 heads (iii) At…
Browse by topic:Statistics
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp