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Two Cards Are Drawn Together from a Pack of 52 Cards. the Probability that One is a Spade and One is a Heart, is - Mathematics

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MCQ

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is

Options

  • `3/20`

  • `29/34`

  • `47/100`

  • `13/102`

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Solution

`13/102`

Explanation:
Let S be the sample space.

Then, n(S) = `""^52C_2=((52xx51))/((2xx1))=1326`

Let E = event of getting 1 spade and 1 heart.
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13.

= `(""^13C_1xx""^13C_1)`

= (13 x 13) = 169

∴ P(E) = `(n(E))/(n(S))`

= `169/1326=13/102`

Concept: Probability (Entrance Exam)
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