All queens, jacks and aces are removed from a pack of 52 playing cards. The remaining cards are well-shuffled and one card is picked up at random from it. The probability of that card to be a king is :
Answer: The probability of that card to be a king is .
Step-by-step solution
Step 1: Determine initial number of cards
We start with a standard deck of 52 playing cards. This is our initial sample space before any cards are removed.
Step 2: Calculate cards removed
The problem states that all queens, jacks, and aces are removed. Since there are 4 suits, there are 4 queens, 4 jacks, and 4 aces, totaling 12 cards removed from the deck.
Step 3: Calculate remaining cards
To find the number of cards left in the deck, we subtract the 12 removed cards from the initial 52 cards.
Step 4: Identify favorable outcomes
We are looking for the probability of picking a king. A standard deck has 4 kings (one for each suit), and kings were not among the cards removed.
Step 5: Calculate probability
The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, there are 4 kings (favorable outcomes) and 40 remaining cards (total possible outcomes).
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