The probability of a seed germinating is 1/3. If three of the seeds are planted,what is the probability that
A.none will germinate
B.at least one will germinagerminate
C. Only one will germinate?
Probability of a seed germinating means the probability of one seed germinating
P(G)=1/3
P(not germinate)=1-1/3
=2/3
(a)P(none germinate)=2/3*2/3*2/3=8/27
(b)P(atleast one)
using a tree diagram
P(GGG or GGN or GNG or GNN or NGG or NGN or NNG)
(1/3*1/3*1/3) + (1/3*1/3*2/3) + (1/3*2/3*1/3) + (1/3*2/3*2/3) + (2/3*1/3*1/3) + (2/3*1/3*2/3) + (2/3*2/3*1/3)
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To find the probabilities, we need to use the concept of probability calculations. The probability calculation formula is:
P(event) = Number of favorable outcomes / Total number of possible outcomes
Let's calculate the probabilities for the given scenarios:
A. None will germinate:
To find the probability that none of the seeds will germinate, we need to calculate the probability that each seed will not germinate. Since the probability of a seed germinating is 1/3, the probability of a seed not germinating is 1 - 1/3 = 2/3.
P(none will germinate) = (2/3) * (2/3) * (2/3) = 8/27
So, the probability that none of the seeds will germinate is 8/27.
B. At least one will germinate:
To find the probability that at least one seed will germinate, we need to calculate the complement of the event that none will germinate.
P(at least one will germinate) = 1 - P(none will germinate) = 1 - 8/27 = 19/27
So, the probability that at least one seed will germinate is 19/27.
C. Only one will germinate:
To find the probability that only one seed will germinate, we need to consider three different cases: the first seed germinates while the other two do not, the second seed germinates while the other two do not, or the third seed germinates while the other two do not.
P(only one will germinate) = (1/3) * (2/3) * (2/3) + (2/3) * (1/3) * (2/3) + (2/3) * (2/3) * (1/3) = 12/27 = 4/9
So, the probability that only one seed will germinate is 4/9.
G = p(germinate) = 1/3 ... N = p(not germinate) = 2/3
this is a binomial probability ... (N + G)^3 = N^3 + 3 N^2 G + 3 N G^2 + G^3
A. the 1st term ... (1/3)^3
B. 1 - 1st term
C. 2nd term ... 3 * (1/3)^2 * (2/3)
It should be C. If there are three, and the probability is one third, that means that one out of every three will germinate.
For three seeds on will germinate
For six seeds two will germinate
For nine seeds three will germinate
For twelve seeds four will germinate , and so on for each multiple of three, whatever number that it is multiplied , that is how many seeds would germinate.