Shopping Mall Promotion A shopping mall has set up a...

Shopping Mall Promotion A shopping mall has set up a promotion as follows. With any mall purchase of $$\$ 50$$ or more, the customer gets to spin the wheel shown here. If a number 1 comes up, the customer wins $$\$ 10$$. If the number 2 comes up, the customer wins $$\$ 5 ;$$ and if the number 2 comes up, the customer wins a discount coupon. Find the following probabilities. a. The customer wins $$\$ 10$$. b. The customer wins money. c. The customer wins a coupon. (Figure can't copy)

Shopping Mall Promotion A shopping mall has set up a promotion as follows. With any mall purchase of $$\$ 50$$ or more, the customer gets to spin the wheel shown here. If a number 1 comes up, the customer wins $$\$ 10$$. If the number 2 comes up, the customer wins $$\$ 5 ;$$ and if the number 2 comes up, the customer wins a discount coupon. Find the following probabilities.
a. The customer wins $$\$ 10$$.
b. The customer wins money.
c. The customer wins a coupon.
(Figure can't copy)

Key Concepts

Union of Events

The union of events refers to the situation where an event can occur in several mutually exclusive ways. For example, winning any cash prize might include several separate outcomes, and their probabilities can be added together because they do not overlap.

Equally Likely Outcomes

When it is assumed that every segment or outcome on the wheel has the same chance of occurring, the outcomes are considered equally likely. This simplifies the calculation of probabilities because the probability of any event can be calculated as the ratio of favorable outcomes to the total outcomes.

Counting Methods

Counting methods involve determining the number of favorable outcomes and the total number of outcomes. This ratio is then used to calculate the probability of an event, which is crucial when assessing promotions or games of chance.

Sample Space

The sample space is the complete set of all possible outcomes of an experiment. In the context of a promotional spin, the sample space includes every unique result that the wheel can land on.

Probability

Probability is a measure of how likely an event is to occur. In problems like this, probabilities are determined by comparing the number of favorable outcomes for an event to the total number of possible outcomes in the experiment.

Event

An event is a subset of the sample space that consists of outcomes that share a common characteristic. For example, one might define the event of winning a cash prize as the outcomes that result in a monetary reward.

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