Sample Space Statistics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A password consists of one letter (A–E) followed by one digit (1–3). (a) List the entire sample space. (b) How many passwords contain the letter 'C'? (c) What is the probability of randomly generating a password that starts with 'C'?

Solution

  1. 1
    Step 1: (a) Sample space: {A1,A2,A3,B1,B2,B3,C1,C2,C3,D1,D2,D3,E1,E2,E3}. Total = 5×3=155 \times 3 = 15.
  2. 2
    Step 2: (b) Passwords with 'C': {C1,C2,C3} = 3 passwords. (c) P(starts with C)=315=15=0.2P(\text{starts with C}) = \frac{3}{15} = \frac{1}{5} = 0.2.

Answer

(a) 15 passwords total. (b) 3 passwords contain 'C'. (c) P(C)=15P(\text{C}) = \frac{1}{5}.
Listing the sample space for small experiments allows us to count favourable outcomes directly. The probability of an event equals the number of favourable outcomes divided by the total number of equally likely outcomes in the sample space.

About Sample Space

The sample space is the complete set of all possible outcomes for a probability experiment, listed without repetition. It forms the foundation for every probability calculation because the probability of any event is a fraction of the sample space.

Learn more about Sample Space →

More Sample Space Examples

Example 1 easy

List the sample space for rolling a standard six-sided die and flipping a coin simultaneously.

Example 2 medium

A restaurant offers 3 starters (soup, salad, bread), 4 mains (chicken, fish, beef, pasta), and 2 des

Example 4 hard

Two dice are rolled. (a) How many outcomes are in the sample space? (b) How many outcomes give a sum

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