This might be easiest if you list them in a table like the one I'll start for you:ĦNote how the first number of each pair in the table is the row number and the second number is the column number. So the probability of rolling two 5's is the product of probability of rolling one 5 times the probability of rolling one 5:Īnother way to figure this out is to list all the possible rolls of two dice. The probability of two independent events is the product of the probabilities of the two individual events.When you roll two dice, the number you get on one dice in no way influences or changes the number you get on the other dice, the numbers you get are independent events.So the probability of rolling a single die and getting one of those six numbers, like a 5, is 1/6. There are 6 faces on a die and each face has a different number on it.

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The opposite ratio (the number of outcomes not in the event to the number in the event E ′ E ′ to the number in the event E E is called the odds against the event. The ratio of the number of equally likely outcomes in an event E E to the number of equally likely outcomes not in the event E ′ E ′ is called the odds for (or odds in favor of) the event. Comparisons of this type are the focus of this section. In other words, there are 3 losing tickets for every winning ticket. In the case of this game, we would compare the 500,000 wins to the 1,500,000 losses. When we evaluate the risk associated with a game like this, it can be useful to compare the number of ways to win the game to the number of ways to lose. If there are 500,000 winners, then it follows that there are 1,500,000 losing tickets. (credit: “My Scratch-off Winnings” by Shoshanah/Flickr, CC BY 2.0) Learning ObjectivesĪfter completing this section, you should be able to:Ī particular lottery instant-win game has 2 million tickets available. Figure 7.33 Scratch-off lottery tickets, as well as many other games, represent the likelihood of winning using odds.

Odds of 4 out of 5 39