An integer n is randomly selected from the set of all integers from 10 to 59, inclusive. W… — GMAT

An integer $n$ is randomly selected from the set of all integers from $10$ to $59$ , inclusive. What is the probability that $n$ is a prime number whose units digit is $3$ ?

A
$\frac{1}{10}$
B
$\frac{4}{49}$
$\frac{2}{25}$ Answer
D
$\frac{2}{23}$
E
$\frac{3}{50}$

Answer

The probability that the selected integer is a prime number whose units digit is

3

\frac{2}{25}

The correct answer identifies that there are 50 total integers in the inclusive range from 10 to 59. Among the numbers ending in 3 (

13, 23, 33, 43, 53

), exactly four are prime (

13, 23, 43, 53

), while 33 is composite. Dividing 4 favorable outcomes by 50 total outcomes yields

\frac{4}{50}

, which simplifies to

\frac{2}{25}

Step-by-Step Solution

Determine the total number of outcomes in the set.

The set contains

59 - 10 + 1 = 50

integers.

For an inclusive set of integers from

a

b

, the total number of integers is

b - a + 1

Identify all integers in the set with a units digit of

3

The candidate integers ending in 3 are

13, 23, 33, 43, 53

These are all two-digit numbers in the range

[10, 59]

ending with

3

Determine which candidate integers are prime numbers.

The prime numbers are

13, 23, 43,

and

53

(a total of 4 favorable outcomes). Note that

33 = 3 \times 11

, so it is composite.

A prime number is an integer greater than 1 that has no positive divisors other than 1 and itself.

Calculate the single-event probability and simplify the fraction.

\text{Probability} = \frac{4}{50} = \frac{2}{25}

Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.

Key Concept

Basic Single-Event Probability

Estimated Time:1m 30s

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