3. An urn contains 20 white balls and 5 green balls. A sample of seven is select

Question

3. An urn contains 20 white balls and 5 green balls. A sample of seven is selected at random. What is the probability that the sample contains at least one green ball?

a) 0.0000

b) 0.5968

c) 1.0000

d) 0.4032

e) 0.8387

f) None of the above.

4. A fair coin is tossed 11 times. What is the probability that the coin lands head at least 9 times?

a) 0.0322

b) 0.0327

c) 0.0317

d) 0.0654

e) 0.0269

f) None of the above.

5.A fair coin is tossed 29 times. What is the probability that at most 27 heads occur?

a) 0.00000076

b) 0.00000006

c) 0.00000081

d) 0.99999994

e) 0.99999919

f) None of the above.

Explanation / Answer

4. A fair coin is tossed 11 times.

Probability to get a head = Probability to get a tail = 1/2

P(X>=9) = Prob of getting a head atleast 9 times
= Prob of getting a head 9 or 10 or 11 times
= 11C9(1/2)^9 (1/2)^2 + 11C10(1/2)^10(1/2)^1 + 11C11(1/2)^11 (1/2)^0
=0.03272

So, Prob of getting atleast 9 heads on the coin is .0327. Answe b) is correct

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