Question

A golf ball is selected at random from a golf bag. If the golf bag contains 1 green balls,6 brown balls, and 8 orange balls, find the probability of the following event. the golf ball is green or brown.

Answer 1

Concepts and reason

Probability:

The ratio of the number of favorable outcomes to certain event and total number of possible outcomes is called as the probability of an event.

Complementary probability:

If an event A is defined, then complement of event A is not occurring of event A.

Mutually exclusive events:

Let A and B be two events. If two or more events of them are not occurring at the same time, then the events are called as mutually exclusive. A and B are said to be mutually exclusive events, when $P\left( {A \cap B} \right) = 0$

Fundamentals

The probability of an event is defined as,

$\begin{array}{c}\\{\rm{Probability}} = \frac{{{\rm{Number}}\,{\rm{of}}\,{\rm{favorable}}\,{\rm{outcomes}}\,{\rm{for}}\,{\rm{an}}\,{\rm{event}}}}{{{\rm{Total}}\,{\rm{number}}\,{\rm{of}}\,{\rm{outcomes}}}}\\\\ = \frac{{N\left( E \right)}}{{N\left( S \right)}}\\\end{array}$

Addition Rule of Probability:

If two events A and B are mutually exclusive, then the probability for event A or event B can be defined as,

$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right)$

The probability that golf ball is green and probability that golf ball is brown is obtained below:

From the given information, bag consists of number of green balls is 1, number of orange balls is 8 and number of brown balls is 6.

Let B be the brown ball, O be the orange ball and G be the green ball.

The total number of balls is,

$\begin{array}{c}\\N\left( S \right) = 1 + 6 + 8\\\\ = 15\\\end{array}$

From the given information, $N\left( G \right) = 1$ and $N\left( S \right) = 15$

The probability that selected ball is green is,

$\begin{array}{c}\\P\left( G \right) = \frac{{N\left( E \right)}}{{N\left( S \right)}}\\\\ = \frac{1}{{15}}\\\\ = 0.0667\\\end{array}$

From the given information, $N\left( B \right) = 6$ and $N\left( S \right) = 15$

Now the probability that selected ball is brown is,

$\begin{array}{c}\\P\left( B \right) = \frac{{N\left( E \right)}}{{N\left( S \right)}}\\\\ = \frac{6}{{15}}\\\\ = 0.40\\\end{array}$

The probability that golf ball is green or brown is obtained as shown below:

From the given information, $P\left( G \right) = \frac{1}{{15}}$ and $P\left( B \right) = \frac{6}{{15}}$ .

The required probability is,

$\begin{array}{c}\\P\left( \begin{array}{l}\\{\rm{Golf ball is }}\\\\{\rm{green or brown}}\\\end{array} \right) = P\left( {G \cup B} \right)\\\\ = P\left( G \right) + P\left( B \right)\\\\ = \frac{1}{{15}} + \frac{6}{{15}}\\\\ = \frac{7}{{16}}\\\\ = 0.4667\\\end{array}$

Ans:

The probability that golf ball is green or brown is 0.4667.