About 10% of the population of a large country is math phobic. If two people are randomly selected what is the probability both are math phobic? And hat is the probability that at least one is math phobic?
Any way to do this on stat crunch?
To calculate the probability of both selected individuals being math phobic, you can use the formula for the probability of independent events. Since the events are independent, the probability can be calculated by multiplying the probability of the first person being math phobic by the probability of the second person being math phobic.
Let's calculate each probability one by one:
1. Probability of the first person being math phobic:
Since 10% of the population is math phobic, the probability would be 10% or 0.1.
2. Probability of the second person being math phobic:
After the first person is selected, the probability of the second person being math phobic remains the same since each person is randomly selected. So, the probability will also be 10% or 0.1.
Now, to calculate the probability of both individuals being math phobic, multiply the probabilities together:
Probability = 0.1 * 0.1 = 0.01 or 1%.
To calculate the probability that at least one person is math phobic, you need to calculate the complement of the probability that neither person is math phobic.
Probability of neither person being math phobic:
Since 10% of the population is math phobic, this means 90% of the population is not math phobic. So, the probability of the first person not being math phobic is 90% or 0.9, and the probability of the second person not being math phobic is also 0.9.
To find the probability of neither person being math phobic, multiply the probabilities together:
Probability of neither person being math phobic = 0.9 * 0.9 = 0.81 or 81%.
Therefore, the probability that at least one person is math phobic is the complement of the probability of neither person being math phobic:
Probability of at least one person being math phobic = 1 - 0.81 = 0.19 or 19%.
I'm not sure whether StatCrunch specifically has a function for step-by-step calculations, but you can use the formulas and values provided above to calculate the probabilities manually using StatCrunch or any other statistical software.
To find the probability of both people being math phobic, we need to consider that each selection is independent. This means that the probability of the first person being math phobic does not affect the probability of the second person being math phobic.
Given that 10% of the population is math phobic, the probability of selecting one math phobic person is 10% or 0.10. Therefore, the probability that both people are math phobic can be calculated as the product of the individual probabilities.
P(both are math phobic) = P(first person math phobic) * P(second person math phobic)
P(both are math phobic) = 0.10 * 0.10 = 0.01 or 1%
Now, to find the probability that at least one person is math phobic, you can consider the complementary event.
The complementary event is when neither person is math phobic. Since the probability that a person is not math phobic would be 1 minus the probability that they are math phobic, we can calculate:
P(at least one math phobic) = 1 - P(neither is math phobic)
P(at least one math phobic) = 1 - (1 - P(first person math phobic)) * (1 - P(second person math phobic))
P(at least one math phobic) = 1 - (1 - 0.10) * (1 - 0.10)
P(at least one math phobic) = 1 - 0.90 * 0.90 = 0.19 or 19%
Now, regarding your question about Stat Crunch, it is a statistical software that can be used for data analysis and probability calculations. While I cannot provide you with step-by-step instructions specific to Stat Crunch, you can use its features to perform calculations related to probability, such as multiplying probabilities and finding complementary probabilities.
States* I think- I don't know what you were trying to spell-
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Both = .10 * .10 = ?
"at least one" indicates either one or both.
One = .10 * (1-.10) = ?
Either-or probabilities are found by adding the individual probabilities.