A quality control analyst randomly selects one component from a shipment containing compon… — GMAT

A quality control analyst randomly selects one component from a shipment containing components labeled with distinct integer batch numbers from $21$ to $100$ , inclusive. What is the probability that the batch number of the selected component is a prime number?

A
$\frac{1}{5}$
$\frac{17}{80}$ Answer
C
$\frac{17}{79}$
D
$\frac{9}{40}$
E
$\frac{17}{63}$

Answer

\frac{17}{80}

The total number of batch numbers from 21 through 100 inclusive is given by

100 - 21 + 1 = 80

. The prime numbers in this range are 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97, which count to 17 prime numbers. Dividing the 17 favorable outcomes by the 80 total outcomes gives a probability of

\frac{17}{80}

Step-by-Step Solution

Determine the total number of components (the sample space size).

Total components

N = 100 - 21 + 1 = 80

For an inclusive range of integers from

a

b

, the number of elements is

b - a + 1

Identify all prime numbers between

21

and

100

, inclusive.

The prime numbers in this range are:

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

. There are

17

prime numbers in total.

Each listed number has exactly two distinct positive divisors:

1

and itself.

Calculate the probability of selecting a prime batch number.

P(\text{Prime}) = \frac{\text{Number of Prime Batch Numbers}}{\text{Total Number of Batch Numbers}} = \frac{17}{80}

Probability of a single event is the ratio of favorable outcomes to total possible outcomes.

Key Concept

Basic Single-Event Probability

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic