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Difficulty: EasySingle Event Probability

A deck of flashcards used for language training contains 5050 cards. There are 1515 vocabulary cards, 2525 grammar cards, and 1010 phrase cards. If a student randomly selects one card from the deck to study, what is the probability that it is a vocabulary card?

  1. 310\frac{3}{10}Answer
  2. B
    37\frac{3}{7}
  3. C
    710\frac{7}{10}
  4. D
    12\frac{1}{2}

Answer

310\frac{3}{10}
The correct answer is found by dividing the number of vocabulary cards by the total number of cards in the deck. There are 1515 vocabulary cards out of 5050 total cards. The fraction 1550\frac{15}{50} simplifies to 310\frac{3}{10} when both the numerator and denominator are divided by their greatest common factor, 55.

Step-by-Step Solution

1
Identify the total number of possible outcomes.
Total cards = 5050
The denominator of a probability fraction is the total number of items in the set.
2
Identify the number of favorable outcomes.
Vocabulary cards = 1515
The question asks specifically for the probability of drawing a vocabulary card.
3
Set up the probability fraction and simplify.
1550=310\frac{15}{50} = \frac{3}{10}
Probability is the ratio of favorable outcomes to total outcomes, and fractions should be reduced to their simplest form.

Key Concept

Calculating single event probability as the ratio of favorable outcomes to the total number of possible outcomes.
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Topics

Single Event Probability

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