
You roll three dice. What is the probability of rolling at least two of the same number? (See Example 3 and Example 4.)

The probability that all three numbers are different is
So, the probability that at least two numbers are the same is
In other words, if you rolled 3 dice 1000 times, you would expect at least two numbers to be alike around 444 times.
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You roll five dice. What is the probability of rolling at least two of the same number? (See Example 3 and Example 4.)
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You roll six dice. What is the probability of rolling at least one odd number? (See Example 3 and Example 4.)

The probability that all six numbers are even is
So, the probability that at least one number is odd is
In other words, if you rolled 6 dice 1000 times, you would expect at least one number to be odd about 984 times.
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You roll seven dice. What is the probability of rolling at least two of the same number? (See Example 3 and Example 4.)
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There are 26 marbles in a bag. The graph shows the color distribution of the marbles. Assume that you randomly draw one marble from the bag and you put the marble back before drawing another.
You randomly draw three marbles from the bag. What is the probability that none of the marbles are red? (See Example 3 and Example 4.)

The probability that none of the marbles are red is
In other words, if you drew 3 marbles from the bag 1000 times, you would expect none of the marbles to be red about 455 times.
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There are 26 marbles in a bag. The graph shows the color distribution of the marbles. Assume that you randomly draw one marble from the bag and you put the marble back before drawing another.
You randomly draw five marbles from the bag. What is the probability that none of the marbles are yellow? (See Example 3 and Example 4.)
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There are 26 marbles in a bag. The graph shows the color distribution of the marbles. Assume that you randomly draw one marble from the bag and you put the marble back before drawing another.
You randomly draw four marbles from the bag. What is the probability that at least one of the marbles is green? (See Example 3 and Example 4.)

The probability that none of the marbles are green is
So, the probability that at least one of the marbles is green is
In other words, if you drew 4 marbles from the bag 1000 times, you would expect at least one of the marbles to be green about 770 times.
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There are 26 marbles in a bag. The graph shows the color distribution of the marbles. Assume that you randomly draw one marble from the bag and you put the marble back before drawing another.
You randomly draw six marbles from the bag. What is the probability that at least one marble is blue? (See Example 3 and Example 4.)
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