Please help I don't get how to do this!
A spinner has three congruent sectors colored orange, green, and purple.
Use the rule of probability of each event.
a) landing on orange, then landing on purple
b) landing on the same color 2 times in a row.
since the events are independent, each spin has a 1/3 chance of being any given color.
So, that's a 1/3 * 1/3 = 1/9 chance of hitting any two given colors in sequence.
For hitting the same color twice, there's a 1/1 chance of hitting *some* color on the first spin. Then, there's a 1/3 chance of hitting the same color next time, so that's 1 * 1/3 = 1/3 chance.
To solve these problems, we need to understand the basic concept of probability. Probability is a measure of the likelihood of an event occurring. It is usually expressed as a fraction or a decimal between 0 and 1.
In this case, we have a spinner with three congruent sectors colored orange, green, and purple. Since each sector is congruent, it means that the chances of the spinner landing on any particular color are equal.
a) To find the probability of landing on orange and then landing on purple, we can multiply the individual probabilities. Since there are three equal sectors, the probability of landing on orange is 1/3, and the probability of landing on purple is also 1/3.
So, the probability of landing on orange and then landing on purple is: (1/3) * (1/3) = 1/9.
b) To find the probability of landing on the same color twice in a row, we need to consider that there are three different colors (orange, green, and purple) and each has an equal chance of occurring.
The probability of landing on any particular color on the first spin is 1/3. The probability of landing on the same color on the second spin is also 1/3 because the spinner has been reset after the first spin.
So, the probability of landing on the same color twice in a row is: (1/3) * (1/3) = 1/9.
Remember, in these types of problems, it is essential to understand the conditions and events involved and determine the individual probabilities of each event occurring. Then, you can use basic arithmetic operations like addition, multiplication, etc., to find the probability of the combined events.