1. ## A probability question

consider a set of one hundred cards labeled from 00 to 99. Draw 16 cards randomly WITH replacement.
a) what is the probability that both"8" & "9" do not appear in the cards drawn

b) what is the probability that "9" appears in the cards drawn?

c) what is the probability that both "9" & "8" appear in the card drawn?

2. Originally Posted by chicory
consider a set of one hundred cards labeled from 00 to 99. Draw 16 cards randomly WITH replacement.
a) what is the probability that both"8" & "9" do not appear in the cards drawn

b) what is the probability that "9" appears in the cards drawn?

c) what is the probability that both "9" & "8" appear in the card drawn?
Are you referring to the 08 and 09 cards or just cards with 8 and/or 9 in any position?

There are two cards 08 and 09, so on any draw the probability of drawing one or other of these is 2/100=1/50, and the probability that neither are drawn is 49/50. Since you are drawing with replacement this probability is the same for each draw.

So what is the probability that in 16 draws neither appear? (these are 16 independent draws each with the same probability of not drawing the 08 or 09 cards)

CB

3. When you wrote, "Draw 16 cards randomly WITH replacement" I assume you meant draw a card randomly and then put it back in the deck 16 times. If that's correct then:

a $\displaystyle (\frac{98}{100})^{16}\approx 07238=72.38\%$

b.How many times? At least once or exactly once?

if exactly once then:

X~binomial(16, 0.02)

$\displaystyle pr(X=1)={{16}\choose{1}}(0.01)(0.99)^{15}\approx 0.1376=13.76\%$

if at least once:

$\displaystyle 1-pr(X=0)={{16}\choose{0}}(0.01)^{0}(0.99)^{16}\appr ox 0.1485=14.85\%$

c.$\displaystyle 1-(\frac{98}{100})^{16}\approx 0.2762=27.62\%$

Let me know if I made any mistakes. Thanks

4. That is either "8" appear in decimal or unit digit and it is same as "9" digit.

Thank you