Drawing a blue tile from a bag and then drawing a red tile without replacing the first tile.
Dependent
Independent
Dependent: The probability of drawing a red tile is dependent on whether a blue tile has already been drawn. If a blue tile has been drawn, the probability of drawing a red tile decreases because there is one less red tile in the bag.
Independent: The probability of drawing a blue tile does not affect the probability of drawing a red tile. The two events are independent of each other, meaning the probability of drawing a red tile remains the same regardless of whether a blue tile has already been drawn.
Suppose that two M&M’s are drawn from a bag of M&M’s that contains 5 green M&M’s and 9 blue M&M’s. What is the probability that you draw a green M&M and then another green M&M WITHOUT replacement?
P(green, green) = __________
5/49
25/182
25/196
10/91
To calculate the probability of drawing a green M&M and then another green M&M without replacement, we can use the formula:
P(green, green) = (Number of ways to draw a green M&M and then another green M&M) / (Total number of possible outcomes)
We have 5 green M&M's and 9 blue M&M's in the bag, so the total number of M&M's in the bag is 5 + 9 = 14.
For the first draw, the probability of drawing a green M&M is 5/14, because there are 5 green M&M's out of a total of 14 M&M's.
After one green M&M has been drawn, there are now 4 green M&M's left out of a total of 13 M&M's.
For the second draw, the probability of drawing another green M&M, without replacement, is 4/13.
Therefore, the probability of drawing a green M&M and then another green M&M without replacement is (5/14) * (4/13) = 20/182 = 10/91.
So, the correct answer is 10/91.
Suppose that two M&M’s are drawn from a bag of M&M’s that contains 5 green M&M’s and 9 blue M&M’s. What is the probability that you draw a green M&M and then a blue M&M WITH replacement?
P(green, blue) = ________
45/182
45/196
81/196
25/196
To calculate the probability of drawing a green M&M and then a blue M&M with replacement, we can use the formula:
P(green, blue) = (Probability of drawing a green M&M) * (Probability of drawing a blue M&M)
For the first draw, the probability of drawing a green M&M is 5/14, because there are 5 green M&M's out of a total of 14 M&M's.
For the second draw, even if the first M&M drawn is green, the probability of drawing a blue M&M (with replacement) remains the same at 9/14 because the M&M's are not depleted or changed in the bag.
Therefore, the probability of drawing a green M&M and then a blue M&M with replacement is (5/14) * (9/14) = 45/196.
So, the correct answer is 45/196.
In your own words, explain the difference of independent and dependent events.
Independent events are events where the occurrence or outcome of one event does not affect the occurrence or outcome of another event. In other words, the probability of an independent event remains the same regardless of what happens in previous events. For example, flipping a coin twice and getting heads on the first flip does not affect the probability of getting heads on the second flip.
On the other hand, dependent events are events where the occurrence or outcome of one event does affect the occurrence or outcome of another event. The probability of a dependent event is influenced by previous events. For example, drawing cards from a deck without replacement is a dependent event because the probability of drawing a certain card changes after each card is drawn.
In summary, with independent events, the outcome of one event does not affect the outcome of subsequent events, while with dependent events, the outcome of one event does impact the outcome of subsequent events.