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Answer: Required Probability = 153,947/201,600 = 0.76363
Explanation:
Let S: An attempt from a cell phone calling another cell number. This is Successful attempt. In this case, two cell phones can be labeled. In the best case, 3 cells can be labeled (when 3 cells remain that are to be labeled)
Let F: An attempt from a cell phone calling its number.
That is Failure. In this case, only one cell can be labeled as we will know that we are calling the same number as the cell phone In the best case, 2 cells can be labeled (when 2 cells remain that are to labeled)
The task can be done in 5 attempts if atleast 4 attempts are successful.So, cases in which task can be done:
A) S S S S S
B) S S S S F
C) S S S F S
D) S S F S S
E) S F S S S
F) F S S S S
If x cells remain that are to be labeled:
P(S) = (x-1)/x
P(F) = 1/x
P(A)=9/10*7/8*5/6*3/4*1/2
P(B)=9/10*7/8*5/6*3/4*1/2
P(C)=9/10*7/8*5/6*1/4*2/3
P(D)=9/10*7/8*1/6*4/5*2/3
P(E)=9/10*1/8*6/7*4/5*2/3
P(F)=1/10*8/9*6/7*4/5*2/3
So, Probability that the task is done in 5 attempts
= P(A)+P(B)+P(C)+P(D)+P(E)+P(F)
=153,947/201,600 = 0.76363 |
