A) \[\frac{1}{4}\]
B) \[\frac{1}{16}\]
C) \[\frac{7}{16}\]
D) \[\frac{9}{16}\]
Correct Answer: C
Solution :
Let the friends come to the restaurant at 5h x min. and 5h y min., respectively, where \[x,y\in [0,60].\] Hence, the sample space consists of all points (x, y) lying in \[60\times 60\]square as shown above and for favourable cases, \[\left| x-y\text{ } \right|\le 15,\] that is \[-15\le x-y\le 15\] which is shown by shaded region in the graph shown below: |
Hence, the probability that they will meet \[=1-\frac{2\times \frac{1}{2}\times 45\times 45}{60\times 60}=1-{{\left( \frac{3}{4} \right)}^{2}}=\frac{7}{16}\] |
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