Question
4)) You pick a card at random. Without putting the first card back, you pick a second card at
random.
4)) What is the probability of picking an even number and then picking an even number?
Write your answer as a fraction or whole number.
Submit
random.
4)) What is the probability of picking an even number and then picking an even number?
Write your answer as a fraction or whole number.
Submit
Ask by Rogers Graham. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of picking an even number twice in a row is
Solution
-
Assume the deck has 10 cards numbered
. The even numbers among these are and ; there are 5 even-numbered cards. -
The probability of picking an even card on the first pick is
-
After removing one even card, there are now
cards left and only of them are even. Thus, the probability of picking an even card on the second pick is -
The probability of both events occurring (picking an even card and then another even card) is the product of the two probabilities:
The final answer is
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Simplify this solution Mind Expander
To determine the probability of picking an even number and then another even number from a standard deck of cards, we first note that there are 52 cards total. In a standard deck, there are 20 even-numbered cards (2, 4, 6, 8, 10 in each suit).
When you pick the first even card, the probability is 20/52. After picking the first card, there are now 51 cards remaining, and if you picked an even card, there are 19 even cards left. The probability of picking a second even card is 19/51.
So, the combined probability of both events happening is:
(20/52) * (19/51) = 380/2652, which simplifies to 5/34.
(20/52) * (19/51) = 380/2652, which simplifies to 5/34.
Therefore, the final probability is 5/34.
