A box contains 20 cards numbered sequentially from 1 through 20, inclusive. If one card is… — GMAT

A box contains 20 cards numbered sequentially from 1 through 20, inclusive. If one card is drawn at random from the box, what is the probability that the number on the drawn card is a prime number? Express your answer as a decimal.

Answer: 0.4

Answer

0.4

The total number of possible outcomes when selecting one card from 20 is 20. The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, and 19, giving 8 favorable outcomes (remembering that 1 is not prime). The single-event probability is calculated by dividing the number of favorable outcomes by the total number of outcomes, yielding

8 / 20 = 0.4

Step-by-Step Solution

Determine the total number of possible outcomes in the sample space.

The sample space consists of 20 equally likely outcomes (integers 1 through 20).

Calculating single-event probability requires establishing the size of the total outcome space

N

Count the number of prime numbers in the set

\{1, 2, \dots, 20\}

There are 8 prime numbers:

\{2, 3, 5, 7, 11, 13, 17, 19\}

By definition, a prime number is an integer greater than 1 with exactly two positive divisors: 1 and itself. Thus, 1 is excluded.

Compute the probability using

P(E) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}

P = \frac{8}{20} = 0.4

Directly apply the basic single-event probability formula.

Key Concept

Basic Single-Event Probability and Prime Number Identification

Estimated Time:45s

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