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A dice is thrown twice and the sum of the numbers appearing is

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A dice is thrown twice and the sum of the numbers appearing is observed to be $8$ . What is the conditional probability that the number $5$ has appeared at least once ?

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A dice is thrown twice and the sum of the numbers appearing is observed to be

8

. What is the conditional probability that the number

5

has appeared at least once ?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Given a dice is thrown twice

⟹

Total Number of outcomes is

n (S) = 6 \times 6 = 36

Let

A

be the event that sum of the numbers appearing on the dice is

8

The favourable outcomes of

A

are

{(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

⟹ n (A) = 5

Let

B

be the event that the number

5

has appeared atleast once

The favourable outcomes of

B

are

{(1, 5), (2, 5), (2, 5), (4, 5), (5, 5), (6, 5), (5, 6), (5, 4), (5, 3), (5, 2), (5, 1)}

⟹ n (B) = 11

Hence Probability of

A

to happen is

P (A) = \frac{n ( A )}{n ( S )} = \frac{5}{36}

Probability of

B

to happen is

P (B) = \frac{n ( B )}{n ( S )} = \frac{11}{36}

The outcomes of

A \cap B

will be

{(3, 5), (5, 3)}

⟹ P (A \cap B) = \frac{n ( A \cap B )}{n ( S )} = \frac{2}{36}

P (B / A) = \frac{P ( A \cap B )}{P ( A )} = \frac{2/36}{5/36} = \frac{2}{5}

P (B / A)

is the probability such that atleast once

5

has to be appeared given that sum of numbers on the dice is

8

So the required conditional probability is

\frac{2}{5}

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Question Text	A dice is thrown twice and the sum of the numbers appearing is observed to be $8$ . What is the conditional probability that the number $5$ has appeared at least once ?
Answer Type	Text solution:1
Upvotes	150

A dice is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once ?

Text solutionVerified

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A dice is thrown twice and the sum of the numbers appearing is observed to be $8$ . What is the conditional probability that the number $5$ has appeared at least once ?