In how many ways can you arrange the books A, B, C, and D on a bookshelf if books A and C must remain neighboring?
1 answer:
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<h2>Answer:</h2>
(a)
The probability is : 1/2
(b)
The probability is : 1/2
<h2>Step-by-step explanation:</h2>The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.
The total combinations that are possible are:
(1,2) (1,3) (1,4) (1,5)
(2,1) (2,3) (2,4) (2,5)
(3,1) (3,2) (3,4) (3,5)
(4,1) (4,2) (4,3) (4,5)
(5,1) (5,2) (5,3) (5,4)
i.e. the total outcomes are : 20
(a)
Let A denote the event that the first number is 4.
and B denote the event that the sum is: 9.
Let P denote the probability of an event.
We are asked to find:
P(A|B)
We know that it could be calculated by using the formula:
Hence, based on the data we have:
( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )
and
( since, there are just two outcomes such that the sum is: 9
(4,5) and (5,4) )
Hence, we have:
(b)
Let A denote the event that the first number is 3.
and B denote the event that the sum is: 8.
Let P denote the probability of an event.
We are asked to find:
P(A|B)
Hence, based on the data we have:
( since, the only outcome out of 20 outcomes is: (3,5) )
and
( since, there are just two outcomes such that the sum is: 8
(3,5) and (5,3) )
Hence, we have: