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Question 144869This question is from textbook
: Could I get help with this pz.thx
experiments and probabilities
2. Explain what outcomes of an experiment are. What does it mean to have equally likely outcomes? Provide ex-amples to illustrate
This question is from textbook
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Whatever happens when you actually perform the experiment is an outcome. Equally likely outcomes are exactly what it says, no possible outcome is any more likely to occur than any other.
Let's use a deck of cards as an example.
The experiment will be to draw one card from a standard deck of 52 cards and the outcome will be the suit of the card drawn. Since there are 13 of each suit in the deck, the likelyhood of drawing a heart is equal to the likelyhood of drawing a card of any other suit. This is an example of equally likely outcomes, and if you replace the drawn card into the deck before repeating the experiment, the likelyhood of any given suit appearing will remain equal to the likelyhood of any other suit.
Now, let's change the experiment a bit. Let's say that you are going to draw a card from a standard deck of 52 cards, again the outcome is the suit of the card, but then you are going to set the drawn card aside. When you draw the second card, you will be drawing from a deck of 51. The second draw becomes an experiment with UNequal likelyhoods. Let's say that you drew a spade on the first draw. When you go back to make the second draw, the remaining deck consists of 13 hearts, 13 diamonds, 13 clubs, but only 12 spades. So while the likelyhood of drawing a heart remains equal to the likelyhood of drawing a diamond or a club, it is slightly less likely that you will draw a second spade.
Other examples of equally likely outcomes are:
Flipping a fair coin. Heads is equally likely to Tails. I say a fair coin because someone could melt a little solder to the tail side of a coin making it heavier and making it slightly more likely that heads would come up when that now unfair coin is flipped.
Rolling one die. The numbers 1 through 6 are equally likely outcomes.
Other examples of unequal likelyhood are:
Rolling a pair of dice. You are 6 times more likely to roll a 7 than a 2, for example.
Drawing 5 cards from a deck of cards: You are many thousands of times more likely to have only a pair than you are likely to have a royal flush.
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