Question

a)

Imagine that a probability of getting 90 and above on any given exam in this STATS course is 5%. What is the probability that you will get 90% or above on all the three exams?

b)

Why is it a good idea to buy two lottery tickets as opposed to one lottery ticket if you want to hit the jackpot? Explain the rationale using the logic of probability, in particular using the language of AND/OR. Which of these (AND/OR) is appropriate in explaining the increased odds.

Answer #1

a.

P(X>=90) = .05

P(X>=90) in all three exams = P(X>=90)^3 = .05^3 = .000125

b. Lets say there are 1000 people playing the lottery and only 1 will be the eventual winner.

Lets say I have bought 1 ticket, which means I have a 1/1000 chance of winning as only 1 ticket is the winner

But if I buy 2 tickets, then my chances of winning become 2/1000, i.e. twice the orignial probability.

So, if you have 2 tickets you have twice chance of winning.

To see how it looks in a formula:

P(win with 2 tickets)

=P(1 ticket) + P(2nd ticket) - P(both ticket)

= 1/1000 + 1/1000 + 0 ( As 2 tickets can't win)

= 2/1000

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