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Total Probability Theorem

If two fair c...

Question

If two fair coins are flipped and at least one of the outcomes is known to be a head. What is the probability that both outcomes are heads?

A

\frac{1}{3}

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B

\frac{1}{4}

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C

\frac{1}{2}

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D

\frac{2}{3}

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Solution

The correct option is A $\frac{1}{3}$
$∵$ It is given that at least one of the outcome is head

So sample space S={(HH), (HT), (TH)}
$n (S) = 3$

Favourable E= {(HH)}
$n (E) = 1$

$H e n c e P (E) = \frac{n (E)}{n (S)} = \frac{1}{3}$

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Similar questions

Q. If two identical coins are tossed for one time simultaneously. Find :

(a) the possible outcomes,

(b) the number of total outcomes,

(c) the probability of getting two heads,

(d) probability of getting at least one head,

(e) probability of getting no heads and

(f) probability of getting only one head.

Ram is about to toss 2 fair coins. If he is asked to find the probability that there is at least 1 head, list the favourable outcomes.

Q. Consider the following experiment:
Step - 1: Flip a fair coin twice.
Step - 2: If the outcomes are (TAILS, HEADS) the output is Y and stop.
Step - 3: If the outcomes are either (heads, heads) or (HEADS, TAILS), then output is N and stop.
Step - 4: If the outcomes are (TAILS, TAILS), then go to Step - 1.
The probability that the output of the experiment is Y is (upto two decimal places)

Q. Consider the following experiment :

Step 1.

Flip a fair coin twice.

Step 2.

If the outcomes are (TAILS, HEADS), then output

Y

Step 3.

If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output

N

Step 4.

If the outcoms are (TAILS, TAILS), then go to

Step 1.

.

The probability that the output of the experiment is

Y

\frac{1}{k}

k

Q. when 2 coins are tossed simultaneously .What are all possible outcomes? In a single throw of 2 coins.what is the probability of getting at least one head?

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