Question

A basket contains $5$ apples and $7$ oranges and another contains $4$ apples and $8$ oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges.
A.$\dfrac{{24}}{{144}}$
B.$\dfrac{{56}}{{144}}$
C.$\dfrac{{68}}{{144}}$
D.$\dfrac{{76}}{{144}}$

Answer 1

Hint : The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Complete step-by-step answer :
Random Experiment: A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty.
Sample Space: The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.
Event: An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E.
We are to find the probability that the fruits are both apples or both oranges.
We know that Probability (event) $= \dfrac{{Number\;of\;Favourable\;outcomes}}{{Total\;n umber\;of\;outcomes}}$
The sample space of the first basket is $5$ apples and $7$ oranges .
The sample space of the second basket is $4$ apples and $8$ oranges.
The probability that both the fruits are apples $= \left( {\dfrac{5}{{12}}} \right).\left( {\dfrac{4}{{12}}} \right) = \dfrac{{20}}{{144}}$
The probability that both the fruits are oranges $= \left( {\dfrac{7}{{12}}} \right).\left( {\dfrac{8}{{12}}} \right) = \dfrac{{56}}{{144}}$
Hence , The probability that the fruits are both apples or both oranges $= \dfrac{{20}}{{144}} + \dfrac{{56}}{{144}}$
$= \dfrac{{76}}{{144}}$
Therefore, option (D) is the correct answer.
So, the correct answer is “Option D”.

Note : The meaning of probability is basically the extent to which something is likely to happen. Probability of any event can be between 0 and 1 only. Probability of any event can never be greater than 1. Probability of any event can never be negative.