Compound Events Statistics Example 1

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

Example 1

easy
A bag contains 3 red and 5 blue marbles. You draw one marble, replace it, then draw another. What is the probability of getting red then blue?

Solution

  1. 1
    Step 1: Since the marble is replaced, the draws are independent events.
  2. 2
    Step 2: P(red)=38P(\text{red}) = \frac{3}{8}, P(blue)=58P(\text{blue}) = \frac{5}{8}.
  3. 3
    Step 3: For independent events: P(red then blue)=P(red)×P(blue)=38×58=1564P(\text{red then blue}) = P(\text{red}) \times P(\text{blue}) = \frac{3}{8} \times \frac{5}{8} = \frac{15}{64}.

Answer

P(red then blue)=1564≈0.234P(\text{red then blue}) = \frac{15}{64} \approx 0.234.
Compound events involve two or more simple events. When events are independent (one does not affect the other), the probability of both occurring is the product of their individual probabilities. Replacement ensures independence between draws.

About Compound Events

Compound events are probability events made up of two or more simple events combined using 'and' (both events occur) or 'or' (at least one occurs). For independent 'and' events, multiply probabilities; for 'or' events, add probabilities and subtract any overlap.

Learn more about Compound Events →

More Compound Events Examples

Example 2 medium

A bag contains 4 red and 6 blue marbles. You draw two marbles without replacement. What is the proba

Example 3 medium

A spinner has sections: Red (50%), Blue (30%), Green (20%). You spin twice. What is the probability

Example 4 hard

A deck has 52 cards. You draw 2 cards without replacement. What is the probability of drawing at lea

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