Question

There are six apples, five oranges, and one pear in John's basket. ​ ​His friend takes three pieces of fruit at random without replacement. ​ ​Determine the probability that all three fruits are taken are apples. ​Write the answer as a fraction.

Answer 1

There is a 9% of chances that all three selections are apples.

Explanation:

We know that there are 6 apples, 5 oranges and 1 pear, which gives a total of 12 fruits, that's total number of possible outcomes, the denominator of the simple probability.

Now, his friend selects three fruits with three trials without replacement, that means we need to find the probability of each even and then multiply them, because they are independent events.

`P=(6)/(12) * (5)/(11) * (4)/(10)=(120)/(1320) \approx 0.09`

Notice that we calculated the total probability using the same expression. The important thing is that you need to decrease the number of events and the total number of outcomes at each selection, because after his friends picks one apple, he doesn't put it back in the bag.

Therefore, there is a 9% of chances that all three selections are apples.

(We multiplies the number by 100 to express it in percentage)