A person rolls a die and picks a card from a deck. What is the probability that the number on the die is even and the card picked is heart given that the card is red.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The person rolls a die and picks a card from a deck of card. A die has 6 sides with the numbers 1, 2, 3, 4, 5 and 6. A standard deck of cards has 52 cards with four suits, clubs and spades that are black and hearts and diamonds that are red.

The probability of any event is the ratio of the number of outcomes favorable to the event and the total number of outcomes.

Here, it is given that the card that is picked is red. This reduces the total number of outcomes to 26 and the number of outcomes favorable to the card that is picked being a heart is 13. The probability that the card is a heart is 13/26 = 1/2. For the die, the probability that the number is even is 3/6 = 1/2.

The combined probability that the person rolls an even number and the card picked is a Heart is 1/2*1/2 = 1/4.

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