Solved Problems on Probability

Problem 1: If a coin is flipped three times, what is the probability of getting exactly two heads?

Solution:

When flipping a coin, there are two possible outcomes for each flip: Heads (H) or Tails (T).

Flipping a coin three times means there are 2³ = 8 possible outcomes.

Favorable outcomes for getting exactly two heads are: HHT, HTH, and THH.

There are 3 favorable outcomes out of 8 possible outcomes.

Using the probability formula:

[Tex]P(Exactly 2 Heads)=\dfrac{Number of favorable outcomes}{Total number of outcomes}=\dfrac{3}{8}[/Tex]

So, the probability of getting exactly two heads is [Tex]( \frac{3}{8} )[/Tex].

Problem 2: In a deck of 52 cards, what is the probability of drawing an ace or a king?

Solution:

A standard deck of cards has 52 cards, with 4 aces and 4 kings.

Event of drawing an ace is mutually exclusive from the event of drawing a king (you can’t draw a card that is both an ace and a king).

Number of favorable outcomes for drawing an ace or a king is (4 + 4 = 8).

Using probability formula:

[Tex]P(Ace or King)=\dfrac{Number of favorable outcomes (Aces + Kings)}{Total number of cards}=\dfrac{8}{52}[/Tex]

Simplifying the fraction [Tex]( \frac{8}{52} )[/Tex] gives us [Tex]( \frac{2}{13} )[/Tex].

So, the probability of drawing an ace or a king is [Tex]( \frac{2}{13} )[/Tex].

Probability is a fascinating and vital field of mathematics that deals with calculating the likelihood of events occurring. It is a concept that permeates our daily lives, from predicting weather patterns to making informed decisions in business and finance. For students, understanding probability is not only crucial for academic success but also for developing analytical skills that are applicable in various real-world scenarios.

In this article, we will discuss how to calculate probability.