1. When I open my mailbox, any piece of mail there has a 90% chance to be junk m
ID: 3334131 • Letter: 1
Question
1. When I open my mailbox, any piece of mail there has a 90% chance to be junk mail. If I get 9 items in my box today, what is the probability that exactly 3 of them are actually interesting (i.e. NOT junk mail)?
2. When I open my mailbox, any piece of mail there has a 90% chance to be junk mail. If I get 9 items in my box today, what is the probability that 3 OR MORE of them are actually interesting (i.e. NOT junk mail)?
3. When I open my mailbox, any piece of mail there has a 90% chance to be junk mail. If I get 9 items in my box today, what is the probability that 3-7 of them are actually interesting (i.e. NOT junk mail)? In other words, what's the probability that I get 3, 4, 5, 6, or 7 pieces of interesting mail in my box?
Explanation / Answer
P(interesting) = 0.1
P(junk mail) = 0.9
P(X) = nCx pxqn-x
1) P(3 interesting out of 9) = 9C3 x 0.13 x 0.96
= 0.0446
2) P(3 or more interesting) = 1 - P(less thyan 3 interesting)
= 1 - 0.99 - 9x0.1x0.98 - 9C2x0.12x0.97
= 1 - 0.3874 - 0.3874 - 0.1722
= 0.0530
3) P(3-7 are interesting) = P(3 or more interesting) - P(8 interesting) - P(9 interesting)
= 0.0530 - 9x0.18x0.9 - 0.19
= 0.5030
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