Mathematics > QUESTIONS & ANSWERS > CS 70 Discrete Mathematics and Probability Theory HW 5 Course Notes | Download for quality grades | (All)

CS 70 Discrete Mathematics and Probability Theory HW 5 Course Notes | Download for quality grades |

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1 Planetary Party (a) Suppose we are at party on a planet where every year is 2849 days. If 30 people attend this party, what is the exact probability that two people will share the same birthday? Y ... ou may leave your answer as an unevaluated expression. (b) From lecture, we know that given n bins and m balls, P no collision ≈ exp(−m 2/(2n)). Using this, give an approximation for the probability in part (a). (c) What is the minimum number of people that need to attend this party to ensure that the probability that any two people share a birthday is at least 0.5? You can use the approximation you used in the previous part. (d) Now suppose that 70 people attend this party. What the is probability that none of these 70 individuals have the same birthday? You can use the approximation you used in the previous parts. Solution: (a) Let’s compute the probability that no two partygoers have the same birthday. We know the second person at the party cannot share a birthday with the first person, the third person at the party cannot share a birthday with the first two, etc. Thus P no collision = 1− 1 28491− 2 28491− 3 2849 ··· 1− 29 2849 Thus P[collision] = 1−P[no collision] = 1− [Show More]

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