A piggy bank contains 60 pennies, 25 nickels, 10 dimes, and...

A piggy bank contains 60 pennies, 25 nickels, 10 dimes, and 5 quarters. If it is equally likely that any one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is: $$ \begin{array}{ll}{\text { a. a penny? }} & {\text { b. a dime? }} \\ {\text { c. not a quarter? }} & {\text { d. a nickel or a dime? }}\end{array} $$

A piggy bank contains 60 pennies, 25 nickels, 10 dimes, and 5 quarters. If it is equally likely that any one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is:
$$
\begin{array}{ll}{\text { a. a penny? }} & {\text { b. a dime? }} \\ {\text { c. not a quarter? }} & {\text { d. a nickel or a dime? }}\end{array}
$$

Key Concepts

Union of Events

The union of events refers to the probability of either one event or another occurring. When events are mutually exclusive, meaning they cannot happen at the same time, the probability of their union is the sum of their individual probabilities. This rule is fundamental in combining events in probability calculations.

Complement Rule

The complement rule in probability states that the probability of an event not occurring is equal to one minus the probability of the event occurring. This concept is useful for scenarios where calculating the probability directly is more complicated than calculating its complement.

Probability Calculation

Probability is calculated as the number of favorable outcomes divided by the total number of outcomes in the sample space. This ratio-based approach is the cornerstone of classical probability, enabling straightforward computations when conditions are equally likely.

Equally Likely Events

Equally likely events are conditions where every outcome in the sample space has the same chance of occurring. This principle allows us to compute probabilities by simply using the ratio of favorable outcomes to the total number of outcomes.

Sample Space

The sample space is the set of all possible outcomes in an experiment. In probability, when dealing with equally likely outcomes, understanding the sample space is essential because it helps define the total number of outcomes that must be considered when calculating probabilities.

Transcript

00:01 Hey guys, in this problem we are given that we have 60 pennies, 25 nickels, 10 dimes, and 5 quarters.

00:07 As i've written up here, just abbreviated them.

00:10 And we are told that they're put in a piggy bank and that we turn it upside down and that one coin falls out.

00:17 And in each part we are asked the probability of a certain thing happening.

00:22 And first, before we do that, just want to make sure that we add up all these things to have to.

00:28 So we already know the total number of coins.

00:31 Total number of coins is 100 coins because it just add them up.

00:35 60 plus 25 is 85.

00:37 85 plus 10 is 95.

00:39 95 plus 5 is 100.

00:40 So there are 100 possible coins.

00:42 And so our first probability question is the probability that a penny fold out.

00:47 So the total possible options of coins available we have is 100, is 100 coins.

00:55 And out of those 100 coins, what's the probability that? a penny falls out well there's 60 pennies so the probability that a penny falls out is 60 over 100 or 0 .06 now similarly we're going to tackle the next part of the problem next part of problem is what's the probability a dime falls out well in order to do that we need to rewrite on the denominator what our total number total coins possible choices are we have 100 possible choices that can fall out.

01:31 And what's the probability that a dime falls out? well, that's going to be the number of dimes divided by the total number of coins, which is 10 divided by 100.

01:42 10 divided by 100 is 0 .01.

01:46 So that is equivalent to the probability of a dime falling out.

01:52 Now we're going to go to part c...

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