Math Problem Statement
Use the method of your choice to determine the following probability. Drawing at least one tenten when you draw a card from a standard deck 3 times (replacing the card each time you draw) Question content area bottom Part 1 The probability is enter your response here. (Round to the nearest thousandth as needed.)
Solution
To determine the probability of drawing at least one "tenten" (which I'll assume refers to a 10 in a standard deck), we can use the complement rule, which is often easier in these types of problems.
Step-by-step approach:
-
Identify the probability of not drawing a 10:
In a standard deck of 52 cards, there are 4 tens (one for each suit). So, the probability of not drawing a 10 is: -
Use complement rule for at least one event:
The probability of drawing at least one ten in 3 draws (with replacement) is the complement of drawing no tens in all 3 draws.The probability of not drawing a 10 in a single draw is . Therefore, the probability of not drawing a 10 in 3 consecutive draws is: We can compute this as:
-
Subtract from 1 to get the complement:
The probability of drawing at least one 10 in 3 draws is: So, let's compute this value.
Now, I'll calculate these values.
The probability of drawing at least one ten in 3 draws (with replacement) is approximately 0.213 (rounded to the nearest thousandth).
Would you like further details or have any questions?
Here are 5 related questions to explore:
- What is the probability of drawing exactly one ten in 3 draws with replacement?
- How does the probability change if you draw without replacement?
- What is the probability of drawing at least two tens in 3 draws with replacement?
- What is the probability of drawing no tens in 5 draws with replacement?
- How would the probability change if there were only 2 tens in the deck?
Tip: In probability, using the complement rule is often simpler for "at least one" scenarios.
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Math Problem Analysis
Mathematical Concepts
Probability
Complement Rule
Formulas
P(not a 10) = (52 - 4) / 52 = 48 / 52 = 12 / 13
P(no 10 in 3 draws) = (12/13)^3
P(at least one 10) = 1 - P(no 10 in 3 draws)
Theorems
Complement Rule
Suitable Grade Level
Grades 9-11
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