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3. Let's play with a fair dodecahedral die (see the previous homework) again. (a) List all prime numbers between 1 and 12. [Note: By definition, 1 is not a prime number.] (b) If you roll this die 10 times, what is the probability that precisely five numbers out of the ten numbers rolled will be prime? [Note: First set up the appropriate numerical expression, and then evaluate it accurate to four decimal places.] (c) If you keep rolling this die until the first prime number appears, what is the probability that you will roll it precisely five times? [Note: First set up the appropriate numerical expression, and then evaluate it accurate to four decimal places.] (d) What is the expected number of times you need to roll it until the first prime number appears?

          3. Let's play with a fair dodecahedral die (see the previous homework) again.
(a) List all prime numbers between 1 and 12. [Note: By definition, 1 is not a prime
number.]
(b) If you roll this die 10 times, what is the probability that precisely five numbers
out of the ten numbers rolled will be prime? [Note: First set up the appropriate
numerical expression, and then evaluate it accurate to four decimal places.]
(c) If you keep rolling this die until the first prime number appears, what is the
probability that you will roll it precisely five times? [Note: First set up the
appropriate numerical expression, and then evaluate it accurate to four decimal
places.]
(d) What is the expected number of times you need to roll it until the first prime
number appears?

3. Let's play with a fair dodecahedral die (see the previous homework) again.
(a) List all prime numbers between 1 and 12. [Note: By definition, 1 is not a prime
number.]
(b) If you roll this die 10 times, what is the probability that precisely five numbers
out of the ten numbers rolled will be prime? [Note: First set up the appropriate
numerical expression, and then evaluate it accurate to four decimal places.]
(c) If you keep rolling this die until the first prime number appears, what is the
probability that you will roll it precisely five times? [Note: First set up the
appropriate numerical expression, and then evaluate it accurate to four decimal
places.]
(d) What is the expected number of times you need to roll it until the first prime
number appears?

Added by Clinton W.

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