Independent Events

Probability Level 1

You flip a coin and roll a die. Let H H be the event you flip a heads and let F F be the event that you roll a 4. What is P ( H ∣ F ) ? P\left(H\ | \ F\right)?

Note: P ( H ∣ F ) P\left(H\ | \ F\right) denotes the probability of H H occurring given that F F occurs.

P ( H ) ⋅ P ( F ) P(H)\cdot P(F) P ( H ) + P ( F ) P(H)+P(F) P ( F ) P(F) P ( H ) P(H)

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Eli Ross by Eli Ross

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1 solution

Eli Ross Staff
Oct 11, 2015

Because the events are clearly independent, P ( H ∣ F ) = P ( H ) . P\left(H\ | \ F\right) = P(H). That is, the event of the 4 being rolled does not change the probability that the heads is flipped!

10 Helpful 0 Interesting 1 Brilliant 0 Confused

Hi, can you please explain in detail what does the symbol "|" mean here? I just assumed it to be P(H,F) and got the wrong answer. Read the note but still confused about what this symbol is called and what it means in other contexts.

Namit Jain - 5 years, 1 month ago

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P(H|P) means probability of H given P

In other words, “if P happens, whats the probability of H happening”

Jerry Christensen - 2 years, 8 months ago

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