Independent Events Math Example 4

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Example 4

easy
A student randomly guesses on two multiple-choice questions, each with 4 options. Find the probability of getting both correct.

Solution

  1. 1
    Each guess has P(correct)=14P(\text{correct}) = \frac{1}{4}; guesses are independent
  2. 2
    Apply multiplication rule: P(both correct)=14×14=116P(\text{both correct}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}

Answer

P(both correct)=116=0.0625P(\text{both correct}) = \frac{1}{16} = 0.0625
When trials are independent, multiply individual probabilities. Guessing on separate questions is independent because the outcome of one question does not affect another.

About Independent Events

Two events are independent if the occurrence of one does not change the probability of the other: P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B).

Learn more about Independent Events →

More Independent Events Examples

Example 1 easy

A fair coin is flipped and a fair die is rolled. Find [formula].

Example 2 medium

For two events [formula] and [formula], [formula] and [formula]. If [formula] and [formula] are inde

Example 3 medium

A coin is flipped and a die is rolled. Find P(heads AND rolling a 6).

Example 5 hard

Events [formula] and [formula] satisfy [formula], [formula], and [formula]. Are [formula] and [formu

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