Compound Events Statistics Example 3

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

Example 3

medium
A spinner has sections: Red (50%), Blue (30%), Green (20%). You spin twice. What is the probability of getting the same colour both times?

Solution

  1. 1
    Step 1: Spins are independent. P(RR)=0.5×0.5=0.25P(\text{RR}) = 0.5 \times 0.5 = 0.25. P(BB)=0.3×0.3=0.09P(\text{BB}) = 0.3 \times 0.3 = 0.09. P(GG)=0.2×0.2=0.04P(\text{GG}) = 0.2 \times 0.2 = 0.04.
  2. 2
    Step 2: P(same colour)=P(RR)+P(BB)+P(GG)=0.25+0.09+0.04=0.38P(\text{same colour}) = P(\text{RR}) + P(\text{BB}) + P(\text{GG}) = 0.25 + 0.09 + 0.04 = 0.38.

Answer

P(same colour)=0.38P(\text{same colour}) = 0.38 (38%).
To find the probability of 'same colour', we add the probabilities of each matching outcome (RR, BB, GG). These are mutually exclusive compound events, so we use the addition rule for the overall probability.

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 1 easy

A bag contains 3 red and 5 blue marbles. You draw one marble, replace it, then draw another. What is

Example 2 medium

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

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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