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A coin is tossed twice. If the outcome is at most one tail, wh

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A coin is tossed twice. If the outcome is at most one tail, what is the probability that both head and tail have appeared?

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A coin is tossed twice. If the outcome is at most one tail, what is the probability that both head and tail have appeared?

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Text solutionVerified

Given a coin is tossed twice

Then the sample space

S

will be

{HH, H T, T H, TT}

Given that the outcome is at most one tail

So favourable outcomes will be

{HH, T H, H T}

Let

A

be the event of getting at most one tail

⟹ n (A) = 3, n (S) = 4

Probability of

A

to happen is

P (A) = \frac{n ( A )}{n ( S )} = \frac{3}{4}

Let

B

be the event that both head and tail had appeared

then the outcomes of

B

is

{H T, T H}

⟹ n (B) = 2

Probability of

B

to happen is

P (B) = \frac{n ( B )}{n ( S )} = \frac{2}{4} = \frac{1}{2}

Favourable outcomes of

A \cap B

is

{H T, T H}

⟹ A \cap B = B

⟹ P (A \cap B) = P (B) = \frac{1}{2}

Required probability is the probability of

B

given that

A

has happen

.. i . e ., P (B / A)

As we know that

P (B / A) = \frac{P ( A \cap B )}{P ( A )} = \frac{\frac{1}{2}}{\frac{3}{4}} = \frac{2}{3}

So Probability that both head and tail have appeared if the the outcome is at most one tail is

\frac{2}{3}

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Question Text	A coin is tossed twice. If the outcome is at most one tail, what is the probability that both head and tail have appeared?
Answer Type	Text solution:1
Upvotes	150