Suppose that we ask n randomly selected people whether they share your birthday. a. Give an expression for the probability that no one shares your birthday (ignore leap years). b. How many people do we need to select so that the probability is at least .5 that at least one shares your birthday?

n = 253 people

Step-by-step explanation:

There are 'n' persons and at least one person should share your birthday, the probability is given by

1 - (364/365)^n

We want this probability to be at least 0.5

Therefore, 1 - (364/365)^n ≥ 0.5

It mathematically becomes:

(364/365)^n ≥ 0.5

Taking In of both sides

In(364/365)^n ≤ In(0.5)

n.In(364/365) ≤ In (0.5)

Therefore,

n ≥ In 0.5/In 364/365

n ≥ 252.652

n = 253

Which implies we need at least 253 people.

rotation point l

step-by-step explanation:

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages