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PLEASE HELP!!!! WILL GIVE BARAINLYIST!!!!

Suppose you select a card at random from a standard deck of cards 60 times, and 12 of those selections are hearts. How does the experimental probability compare to the theoretical probability? Include the difference between both types in your explanation.

2 Answers

4 votes

Answer:

A standard deck is composed of 52 cards, and contains 13 cards per suit. So, the theoretical probability of picking a card of any suit (and thus, in particular, a heart) is given by

On the other hand, the experimental probability is (as the name suggests) the probability that we can deduce from our experiment: we picked 60 cards, and 12 of these were hearts. This means that it would seem to us that

Explanation:

User Akbar Masterpadi
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Experimental probability = 1/5

Theoretical probability = 1/4

note: 1/5 = 0.2 and 1/4 = 0.25

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How I got those values:

We have 12 hearts out of 60 cards total in our simulation or experiment. So 12/60 = (12*1)/(12*5) = 1/5 is the experimental probability. In the simulation, 1 in 5 cards were a heart.

Theoretically it should be 1 in 4, or 1/4, since we have 13 hearts out of 52 total leading to 13/52 = (13*1)/(13*4) = 1/4. This makes sense because there are four suits and each suit is equally likely.

The experimental probability and theoretical probability values are not likely to line up perfectly. However they should be fairly close assuming that you're working with a fair standard deck. The more simulations you perform, the closer the experimental probability is likely to approach the theoretical one.

For example, let's say you flip a coin 20 times and get 8 heads. We see that 8/20 = 0.40 is close to 0.50 which is the theoretical probability of getting heads. If you flip that same coin 100 times and get 46 heads, then 46/100 = 0.46 is the experimental probability which is close to 0.50, and that probability is likely to get closer if you flipped it say 1000 times or 10000 times.

In short, the experimental probability is what you observe when you do the experiment (or simulation). So it's actually pulling the cards out and writing down your results. Contrast with a theoretical probability is where you guess beforehand what the result might be based on assumptions. One such assumption being each card is equally likely.

User Owenfi
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