QQuestionMathematics
QuestionMathematics
In a standard 52 -card deck, half of the cards are red and half are black. The 52 cards are divided evenly into 4 suits: spades, hearts, diamonds, and clubs. Each suit has three face cards (jack, queen, king) and an ace. Each suit also has 9 cards numbered from 2 to 10.
Luis draws 1 card from a deck, 39 times. Predict how many times he draws an ace.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Determine the number of aces in a standard deck
- Total number of aces: $$4 \times 1 = 4$$ aces
- Total cards in a deck: 52 - Number of suits: 4 - Aces per suit: 1
Step 3:: Calculate the probability of drawing an ace in a single draw
- Probability of drawing an ace = $$\frac{4}{52} = \frac{1}{13}
Step 4:: Use the expected value formula for repeated independent draws
- Expected number of aces = $$39 \times \frac{1}{13} = 3
- Number of draws: 39
Final Answer
Explanation: - The expected value represents the average number of times an event occurs in repeated trials - This calculation assumes each draw is independent and the card is replaced or the deck is reshuffled after each draw
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