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A bowl of fruit is on the table. It contains six apples, two oranges, and four bananas. Daniel and Sean come home from school and randomly grab one fruit each. What is the probability that both grab oranges?
##P(O,O) = 2/12 xx 1/11 = 1/66##
For probability questions, think of each event happening separately, it makes the maths easier to understand. For example, in this question, do not think of the two boys taking a fruit at the same time - that makes the maths complicated . Let Daniel take a fruit first, then Sean can take a fruit. There are two parts to consider.
##Probability = "number of desirable outcomes"/"total number of possible outcomes"##
For Daniel: there are 12 different pieces of fruit in the bowl, he just takes one without choosing a specific fruit. (random) The chance that Daniel takes an orange is ##2/12## Of the 12 pieces of fruit. 2 are oranges.
Now Sean: the numbers of fruit in the bowl have changed. There are now only 11 pieces of fruit in the bowl, and only 1 is an orange. The chance that Sean takes an orange is ##1/11##
The probability that BOTH take an orange is:
##P(O) xx P(O) = 2/12 xx 1/11 = 1/66##