How many two digit numbers do not contain the digit 9?
1 answer:
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Answer:
(1) The value of P (A) is 0.4286.
(2) The value of P (B) is 0.50.
(3) The value of P (A ∩ B) is 0.2143.
(4) The the value of P (B|A) is 0.50.
(5) The events <em>A</em> and <em>B</em> are independent.
Step-by-step explanation:
The events are defined as follows:
<em>A</em> = a student in the class has a sister
<em>B</em> = a student has a brother
The information provided is:
<em>N</em> = 210
n (A) = 90
n (B) = 105
n (A ∩ B) = 45
The probability of an event <em>E</em> is the ratio of the favorable number of outcomes to the total number of outcomes.
The conditional probability of an event <em>X</em> provided that another event <em>Y</em> has already occurred is:
If the events <em>X</em> and <em>Y</em> are independent then,
(1)
Compute the probability of event <em>A</em> as follows:
The value of P (A) is 0.4286.
(2)
Compute the probability of event <em>B</em> as follows:
The value of P (B) is 0.50.
(3)
Compute the probability of event <em>A</em> and <em>B</em> as follows:
The value of P (A ∩ B) is 0.2143.
(4)
Compute the probability of <em>B</em> given <em>A</em> as follows:
The the value of P (B|A) is 0.50.
(5)
The value of P (B|A) = 0.50 = P (B).
Thus, the events <em>A</em> and <em>B</em> are independent.
Answer:
a) 10th term is 0.051
b) The sum of first 18 terms of given sequence is 51.48
Step-by-step explanation:
We are given the sequence 26, 13, 6.5, ..... we need to find
a) 10th term
b) Sum of first 18 terms
Before solving we need to determine if the sequence is arithmetic or geometric
The sequence is arithmetic if common difference d is same.
The sequence is geometric if common ratio r is same.
Finding common difference d: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5
As common ratio is same so, the sequence is geometric.
a) Finding common difference: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
a) 10th term
The formula to find 10th term is:
We have a₁=26 and r = 0.5 n=10
So, 10th term is 0.051
b) Sum of first 18 terms
The formula to find sum of geometric series is:
where a= 1st term, r = common ratio and n= number of terms
In the given sequence we have
a=26, r=0.5 and n=18
Finding sum of first 18 terms
So, sum of first 18 terms of given sequence is 51.48