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# You roll a die, flip a coin, and draw a card. What is the probability that:

You roll a 5, flip a Head, and draw an Ace?

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Bill P. | A math tutor that is both knowledgeable and patient in secondary math.A math tutor that is both knowledgeable ...
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Ok, now assuming it is 1/6 for rolling a "5", 1/2 for getting "heads", and 1/13 for drawing an "Ace", what does one do with these fractions:

MULTIPLY THEM !!

(1/6) (1/2) (1/13) = 1/156

If you have a 36-card deck with 4 aces then replace the 1/13 ratio with 1/9

The probability in this case 1/108

Very small chance (less than 1%) either way.

Do not bet on being able to get that result very often.
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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The first two shall be obvious. A dice has 6 possible outcomes, so getting any number has probability 1/6. A coin has two sides, so there are two outcomes, each with probability 1/2, neglecting the tiny probability the coin stands on edge (just kidding!). With the deck of cards it is trickier. If you are talking about the 52 card deck, then there are exactly 4 aces, you may have 4 favorable outcomes out of 52, so your probability is 4/52=1/13. If you are talking about 36-card deck, then it is 4/36=1/9.