Question

A box contains $5$red balls, ${\mathbf{8}}$green balls and ${\mathbf{10}}$pink balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
A. $\dfrac{{13}}{{23}}$
B. $\dfrac{{10}}{{23}}$
C. $\dfrac{{11}}{{23}}$
D. $\dfrac{{13}}{{529}}$

Answer 1

First, we have to find the individual probability of each color and then adding the individual probabilities of green and red.

[\Probability, = ,\dfrac{{Total,outcome,occurred}}{{Total,no.,of,outcome}}]

Complete step by step solution:
Total no. of balls $= 5 + 8 + 10 = 23$
Probability of that when a red ball is drawn at random $= \dfrac{5}{{23}}$
Probability that when a green ball is drawn at random $= \dfrac{8}{{23}}$
Total probability when a drawn ball is either green or red $= \left( {\dfrac{8}{{23}} + \dfrac{5}{{23}}} \right) = \dfrac{{13}}{{23}}$

Thus the correct option is A

Additional Information: Probability is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

Experiment: Any phenomenon like rolling a dice, tossing a coin, drawing a card from a well-shuffled deck, etc.

Outcome: The Result of any event; like number appearing on a dice, side of a coin, drawn out card, etc.

Sample Space: The set of all possible outcomes.

Event: Any combination of possible outcomes or the subset of sample space; like getting an even number on rolled dice, getting a head/tail on a flipped coin, drawing out a king/queen/ace of any suit.

Probability Function: A function giving the probability for each outcome.

Note: Total no. of green and red balls $= 8 + 5 = 13$.
Total no. of balls $= 5 + 8 + 13 = 23$
$\therefore$Total probability that drawn ball is either green or red $= \dfrac{{13}}{{23}}$