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Mathematics

From a pack of 52 playing cards, one card is drawn at random. What is the probability that the card drawn is a ten or a spade?

  1. (126)\Big(\dfrac{1}{26}\Big)

  2. (113)\Big(\dfrac{1}{13}\Big)

  3. (413)\Big(\dfrac{4}{13}\Big)

  4. (1752)\Big(\dfrac{17}{52}\Big)

Probability

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Answer

A standard deck of playing cards contains 52 cards.

Total number of outcomes = 52

There are 13 spade cards and 4 tens in a deck, Ten of Spades is a card that is both a spade and a ten.

Hence, no. of cards that are tens or spades = 13 Spades + 3 Tens

Let E be the event of choosing a ten or a spade , then

The number of favorable outcomes to the event E = 16

∴ P(E) = Number of favorable outcomesTotal number of outcomes=1652=413\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{16}{52} = \dfrac{4}{13}

Hence, option 3 is the correct option.

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