Independent and Dependent Events
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AP Statistics › Independent and Dependent Events
True or False: When 2 cards are drawn without replacement from a regular deck of 52 cards, the event of drawing a heart first independent of the event of drawing a heart second.
False
True
Cannot be determined by the information given.
Sometimes
Explanation
These events are not independent, because if one event happens, it affects the probability of the other event happening. Consider the probability of drawing a heart and the probability of getting a heart given a heart was already drawn. If these two probabilities are the same, the events are independent. If the two probabilities are not the asme, the events are not independent.
After a heart has already been drawn, there are now only 52 cards total and 12 hearts left. These two probabilities are not equal, therefore the events are not independent.
True or False: When 2 cards are drawn without replacement from a regular deck of 52 cards, the event of drawing a heart first independent of the event of drawing a heart second.
False
True
Cannot be determined by the information given.
Sometimes
Explanation
These events are not independent, because if one event happens, it affects the probability of the other event happening. Consider the probability of drawing a heart and the probability of getting a heart given a heart was already drawn. If these two probabilities are the same, the events are independent. If the two probabilities are not the asme, the events are not independent.
After a heart has already been drawn, there are now only 52 cards total and 12 hearts left. These two probabilities are not equal, therefore the events are not independent.
True or false:
A family has 3 boys. The probability that the fourth child will also be a boy is less than 50%
False
True
More information is needed.
Sometimes
Explanation
The gender of each child can be considered an independent event. Each child has a 50% chance of being a boy, and whether a boy was already born previously does not affect the next child's gender.
True or false:
A family has 3 boys. The probability that the fourth child will also be a boy is less than 50%
False
True
More information is needed.
Sometimes
Explanation
The gender of each child can be considered an independent event. Each child has a 50% chance of being a boy, and whether a boy was already born previously does not affect the next child's gender.
True or false: When drawing two cards with replacement, the event drawing a spade first is independent of the event drawing a heart second.
True
False
Sometimes
More information is needed.
Explanation
These two events are independent of one another. During sampling with replacement, the first card does not affect the second card being picked.
To illustrate, consider the probability of drawing a heart first
Assuming you first drew a heart and replaced it in the deck, does the probability of drawing a heart as the second card change?
The probability remains the same, there are still 13 hearts and 52 total cards.
True or false: When drawing two cards with replacement, the event drawing a spade first is independent of the event drawing a heart second.
True
False
Sometimes
More information is needed.
Explanation
These two events are independent of one another. During sampling with replacement, the first card does not affect the second card being picked.
To illustrate, consider the probability of drawing a heart first
Assuming you first drew a heart and replaced it in the deck, does the probability of drawing a heart as the second card change?
The probability remains the same, there are still 13 hearts and 52 total cards.
There are 10 horses in a herd. 4 are males, 6 are females. 7 of the horses are brown while the remaining 3 are white. 5 female horses are brown. A horse is randomly selected from the herd. Given that the horse is brown, what is the probability that the horse is a male?
Explanation
The probability of any event occurring is the number of outcomes in which case that event occurs divided by the number of total number of outcomes. Here you know that the total number of brown horses is 7, and if 5 of those brown horses are female then 2 must be male. So the probability that a brown horse is male is 2/7.
There are 10 horses in a herd. 4 are males, 6 are females. 7 of the horses are brown while the remaining 3 are white. 1 male horse is white, 5 female horses are brown.
A horse is randomly selected from the herd. What is the probability that the horse chosen is brown or female?
Explanation
This problem asks for the probability of one event or another, so the addition rule of probability is approriate. However, brown horse and female horse are not mutually exclusive events, because there are brown female horses. Therefore we must subtract the brown male horses to avoid double counting.
Now, fill in the equation.
There are 10 horses in a herd. 4 are males, 6 are females. 7 of the horses are brown while the remaining 3 are white. 1 male horse is white, 5 female horses are brown.
A horse is randomly selected from the herd. What is the probability that the horse chosen is brown or female?
Explanation
This problem asks for the probability of one event or another, so the addition rule of probability is approriate. However, brown horse and female horse are not mutually exclusive events, because there are brown female horses. Therefore we must subtract the brown male horses to avoid double counting.
Now, fill in the equation.
There are 10 horses in a herd. 4 are males, 6 are females. 7 of the horses are brown while the remaining 3 are white. 5 female horses are brown. A horse is randomly selected from the herd. Given that the horse is brown, what is the probability that the horse is a male?
Explanation
The probability of any event occurring is the number of outcomes in which case that event occurs divided by the number of total number of outcomes. Here you know that the total number of brown horses is 7, and if 5 of those brown horses are female then 2 must be male. So the probability that a brown horse is male is 2/7.