(a)
To calculate: The probability of getting exactly one 6.
The probability of getting exactly one 6 is 0.39.
Given information:
The numbers of trails n is 4 and the numbers outcomes k is 1 and p is the probability of success.
Formula used:
The formula to calculate the binomial probability is given as,
Here, n is the numbers of trails, k is the numbers of outcomes and p is the probability of success.
Calculation:
Since, a dice is rolled, so there may be 6 possible outcomes that are 1,2,3,4,5 and 6.
So, the probability of success p is
The number of successes among a fixed number of independent trials at a constant
Substitute 1 for k ,
Hence, the probability of getting exactly one 6 is 0.39.
(b)
To calculate: The probability of getting exactly two 6.
The probability of getting exactly two 6 is 0.12.
Given information:
The numbers of trails n is 4 and the numbers outcomes k is 2 and p is the probability of success.
Formula used:
The formula to calculate the binomial probability is given as,
Here, n is the numbers of trails, k is the numbers of outcomes and p is the probability of success.
Calculation:
Since, a dice is rolled, so there may be 6 possible outcomes that are 1,2,3,4,5 and 6.
So, the probability of success p is
The number of successes among a fixed number of independent trials at a constant
Substitute 2 for k ,
Solve further,
Hence, the probability of getting exactly two 6 is 0.12.
(c)
To calculate: The probability of getting at least two 6’s.
The probability of getting at least two 6’s is 0.13.
Given information:
The numbers of trails n is 4 and the numbers outcomes k is 0,1 and p is the probability of success.
Formula used:
The formula to calculate the binomial probability is given as,
Here, n is the numbers of trails, k is the numbers of outcomes and p is the probability of success.
Calculation:
Since, a dice is rolled, so there may be 6 possible outcomes that are 1,2,3,4,5 and 6.
So, the probability of success p is
The number of successes among a fixed number of independent trials at a constant
Substitute 0 for k ,
Solve further,
Substitute 1 for k ,
Now, Using the Addition rule for mutually exclusive events:
Using the complement rule
Hence, the probability of getting at least two 6’s is 0.13.
Chapter 10 Solutions
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