The barkleys have a set of plastic picnic cups and dishes that come in 6 different colors. Blue, Red, Green, Yellow , Orange, and Purple.
1. How many possible cup-and-dish combinations can they make with such a set?
2. peter will pick a dish and a cup without looking.What is the probability that she will get and orange plate and a blue cup?
3. Suppose the red cup and the blue dish are accidentally broken. Is the probability of randomly picking an orange plate and a blue cup now greater or smaller? Explain how you know.
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1. To find the number of possible cup-and-dish combinations, we need to multiply the number of choices for the cup by the number of choices for the dish. In this case, there are 6 different colors for both the cup and the dish, so the total number of combinations is 6 multiplied by 6, which equals 36 possible cup-and-dish combinations.
2. To find the probability of selecting an orange plate and a blue cup, we need to calculate the ratio of the number of favorable outcomes to the total number of possible outcomes. Since there is only 1 orange plate and 1 blue cup in the set, there is only 1 favorable outcome. The total number of possible outcomes is 36, as calculated in question 1. Thus, the probability is 1/36.
3. The probability of randomly picking an orange plate and a blue cup is still 1/36 after the red cup and the blue dish are broken. This is because the breakage of these items does not affect the relative frequency of the other items. Each item still has the same probability of being chosen. Since there is still only 1 orange plate and 1 blue cup in the set, the probability remains the same.