Answer: a) [tex]\dfrac{799}{31250}[/tex] b) [tex]\dfrac{30451}{31250}[/tex]
Step-by-step explanation:
Since we have given that
Number of days in a year = 365
Number of students = 50
Probability that no two students share the same birthday. It means each student has different birthday.
Probability(no two students share the same birthday)[tex]=\dfrac{365-1}{365}\times \dfrac{365-2}{365}........\times \dfrac{365-50}{365}[/tex]
Probability(no two students share the same birthday)[tex]=\dfrac{^{365}P_{50}}{365^{50}}[/tex]
Probability(no two students share the same birthday)[tex]=\dfrac{799}{31250}\approx 0.025568[/tex]
Probability that at least one of the students has the same birthday as another student in the class is given by
[tex]1-P(\text{no student share the same birthday})\\\\=1-\dfrac{799}{31250}\\\\=\dfrac{30451}{31250}=0.974432[/tex]
