A basket contains 8 pieces of fruit: 3 apples, 3 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?

1 Answer
Jun 28, 2016

The probability that Jonas will get an orange and Beth will get an apple is #9/56#.

Explanation:

This is the problem relating to conditional probability. This can be derived using multiplication rue, which states that #P[AnnB]=P[A]*P[B|A]#, i.e. probabillity of happening of both the events #A# and #B# is equal to probability of event #A# happening multiplied by probability of happening of event #B#, given #A# event has already happened.

As the basket contains #8# pieces of fruits of which #3# are oranges,

the probability that Jonas will get an orange is #3/8#.

Considering Jonas has already got an orange, as #7# fruits are left of which #3# are apple, probability that Beth will get an apple will be #3/7#.

Hence the probability that Jonas will get an orange and Beth will get an apple is #3/8xx3/7=9/56#.