Given that a randomly chosen card from a standard deck of 52 cards is less than 7, what is the probability it is the 5 of diamonds? Assume that aces are low cards.
Question
Given that a randomly chosen card from a standard deck of 52 cards is less than 7, what is the probability it is the 5 of diamonds? Assume that aces are low cards.
Solution
Step 1: Identify the total number of outcomes
A standard deck of 52 cards consists of 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
Step 2: Identify the favorable outcomes for the card to be less than 7
Cards less than 7 include Ace, 2, 3, 4, 5, 6. Since there are 4 suits, there are 4*6 = 24 cards that are less than 7.
Step 3: Identify the favorable outcome for the card to be the 5 of diamonds
There is only 1 card that is the 5 of diamonds in a standard deck.
Step 4: Calculate the probability
The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the probability that a randomly chosen card less than 7 is the 5 of diamonds is 1/24.
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