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Probability – Independent events

Probability – Independent events


Can you please explain why the answer – Drawing a diamond and drawing an ace is the answer.
I thought the answer is Drawing a Queen and drawing a Jack.
Going back to the card example, which of the following sets of events are independent?

Drawing a Queen and drawing a Jack.

Drawing a Heart and drawing the Jack of Hearts.

Drawing a Diamond and drawing an Ace.

Drawing a four and drawing the Ace of Spades.

1 Answer

365 Team

Hey Astro,

Thanks for reaching out!
In this case, you have to calculate the conditional and unconditional probabilities of each event in each answer to determine this. If they are equal, the events are independent, so you need to compare P(A|B ) and P(A) for every pair of events.
Since P(Diamond) = 1/4 and P(Diamond | Ace) = 1/4, then the two events are independent. Additionally, we can make a double check and see that P(Ace) = 1/13 and P(Ace|Diamond) = 13.
Alternatively, P(Queen) = 1/13, but P(Queen|Jack) = 0 (since the card can’t be a Queen if we know it’s a Jack) and also P(Ace of Spades) = 1/52, but P(Ace of Spades | 4) = 0 and similarly, P(4) = 1/13 but P(4 | Ace of Spades) = 0.

Hope this clears things up!
365 Vik

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