Calculating probabilities is an important skill in genetics. It is used to determine an individual's chance of inheriting genetic diseases, to determine the chances of carrying a disease or genetic trait, as well as for a variety of other tasks, such as predicting the success of a cloning project. When you are trying to calculate the probability of two or more independent events occurring at the same time, use the product rule. An example of this would be the flipping of two coins simultaneously. If we want to calculate the probability of obtaining heads on both flipped coins, we simply take the probability of landing heads on the first coin (1/2) and multiply it by the probability of landing heads on the second coin (1/2). Thus, the probability of landing heads on both coins simultaneously is the product of the individual probabilities: (1/2) × (1/2) = 1/4.
Whenever we are calculating the combined probability resulting from more than one independent event, we use the product rule.
How many different DNA molecules 10 base pairs long are possible?
Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.
How many different kinds of nucleotides make up DNA?
A. |
B. |
C. |
D. |
Calculating probabilities is an important skill in genetics. It is used to determine an individual's chance of inheriting genetic diseases, to determine the chances of carrying a disease or genetic trait, as well as for a variety of other tasks, such as predicting the success of a cloning project. When you are trying to calculate the probability of two or more independent events occurring at the same time, use the product rule. An example of this would be the flipping of two coins simultaneously. If we want to calculate the probability of obtaining heads on both flipped coins, we simply take the probability of landing heads on the first coin (1/2) and multiply it by the probability of landing heads on the second coin (1/2). Thus, the probability of landing heads on both coins simultaneously is the product of the individual probabilities: (1/2) × (1/2) = 1/4.
Whenever we are calculating the combined probability resulting from more than one independent event, we use the product rule.
How many different DNA molecules 10 base pairs long are possible?
Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.
What is the probability of any nucleotide being present at any position in a molecule of DNA?
A. |
B. |
C. |
D. |
When flipping a coin once, the probability of getting heads is 1 out of 2, because it is one possibility (i.e., heads or tails) out of a two-sided coin. Similarly, the probability of rolling a die once and getting a 3 is 1 chance in 6, because a 3 is one possibility out of the six sides of the die. By the same reasoning, the probability of identifying the nucleotide filling one position within a single strand of DNA is 1 out of the-number-of-kinds-of-nucleotides (i.e., the denominator is equal to the answer to Step 1).
Calculating probabilities is an important skill in genetics. It is used to determine an individual's chance of inheriting genetic diseases, to determine the chances of carrying a disease or genetic trait, as well as for a variety of other tasks, such as predicting the success of a cloning project. When you are trying to calculate the probability of two or more independent events occurring at the same time, use the product rule. An example of this would be the flipping of two coins simultaneously. If we want to calculate the probability of obtaining heads on both flipped coins, we simply take the probability of landing heads on the first coin (1/2) and multiply it by the probability of landing heads on the second coin (1/2). Thus, the probability of landing heads on both coins simultaneously is the product of the individual probabilities: (1/2) × (1/2) = 1/4.
Whenever we are calculating the combined probability resulting from more than one independent event, we use the product rule.
How many different DNA molecules 10 base pairs long are possible?
Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.
What is the probability of any combination of two nucleotides being present at any two positions in a molecule of DNA?
A. |
B. |
C. |
D. |
To understand this question, break it into two parts. First ask, what is the probability of any nucleotide being present at position one and, independently, what is the probability of any nucleotide being present at position two? The answer to each of these questions is the same as the answer to Step 2.
Second, in order to answer Step 3, take the two independent probabilities and invoke the product rule. The steps applied here are, in principle, the same as the coin-flipping example that opened this problem.
Calculating probabilities is an important skill in genetics. It is used to determine an individual's chance of inheriting genetic diseases, to determine the chances of carrying a disease or genetic trait, as well as for a variety of other tasks, such as predicting the success of a cloning project. When you are trying to calculate the probability of two or more independent events occurring at the same time, use the product rule. An example of this would be the flipping of two coins simultaneously. If we want to calculate the probability of obtaining heads on both flipped coins, we simply take the probability of landing heads on the first coin (1/2) and multiply it by the probability of landing heads on the second coin (1/2). Thus, the probability of landing heads on both coins simultaneously is the product of the individual probabilities: (1/2) × (1/2) = 1/4.
Whenever we are calculating the combined probability resulting from more than one independent event, we use the product rule.
How many different DNA molecules 10 base pairs long are possible?
Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.
How many different DNA molecules two base pairs long are possible?
A. |
B. |
C. |
D. |
This is the inverse of Step 3. First, consider how many different nucleotides can occupy each of the two sites independently. Second, use the product rule to determine how many different pairs of nucleotides can be made.
Calculating probabilities is an important skill in genetics. It is used to determine an individual's chance of inheriting genetic diseases, to determine the chances of carrying a disease or genetic trait, as well as for a variety of other tasks, such as predicting the success of a cloning project. When you are trying to calculate the probability of two or more independent events occurring at the same time, use the product rule. An example of this would be the flipping of two coins simultaneously. If we want to calculate the probability of obtaining heads on both flipped coins, we simply take the probability of landing heads on the first coin (1/2) and multiply it by the probability of landing heads on the second coin (1/2). Thus, the probability of landing heads on both coins simultaneously is the product of the individual probabilities: (1/2) × (1/2) = 1/4.
Whenever we are calculating the combined probability resulting from more than one independent event, we use the product rule.
How many different DNA molecules 10 base pairs long are possible?
Unpack the Problem: Break this problem into several parts and arrive at a solution using this guided, step-by-step approach.
How many different DNA molecules 10 base pairs long are possible?
A. |
B. |
C. |
D. |
E. |
Recall that in Step 4, the number of possible pairwise combinations was 42. In this question, the number of sites under consideration is 10 instead of two.
General Hints
To Summarize
Whenever you are calculating the combined probability resulting from more than one independent event, use the product rule. When the probability for each event is identical, then the product rule can be written in exponential form. The base is the number of possible outcomes for one event (in this case, the number of kinds of nucleotides that can occupy any one site). The exponent is the number of times the base is multiplied by itself (in this case, it is the number of sites under consideration).