Question

Suppose you roll a single fair die 10 times (all rolls are mutually independent). What is the probability that you roll a 5 in exactly 3 of the 10 rolls?

Answer #1

When a die is rolled the sample space is given by

2.29 Die rolls. You roll a die three times.
what is the probability the sum of the first two rolls is equal to
the third roll?
3.3 Off to the races. Suppose mike places three
separate bets on three separate tracks. Each bet is for a specific
horse to win. His horse in race 1 wins with probability 1/5. His
horse in race 2 with probability 2/5. His horse in race 3 wins with
probability 3/5. What is the probability...

Suppose you roll a fair 100-sided die.
What is the expected number of rolls you would have to make to
roll a 100?
What is the expected number of rolls you would have to make to
have rolled a 98, 99, and 100?

Assume that a fair
six-sided die is rolled 9 times, and the roll is called a success
if the result is in {1,2}{1,2}.
What is the probability that there are exactly 4 successes or
exactly 4 failures in the 9 rolls?

Please Explain!
Roll a fair die five times. What is the probability of seeing a
full house, in the sense that 3 rolls of one type, and two rolls of
another different type? Note that we do not allow the 5 rolls to be
of the same type.

Suppose you plan to roll a fair six-sided die two times. What is
the probability of rolling a ‘1’ both times?
Group of answer choices

You roll a fair die 5 times. What is the probability you get at
least four 6’s? This time you roll the die 204 times. What is the
probability you get between 30 and 40 6’s?

Assume we roll a fair four-sided die marked with 1, 2, 3 and
4.
(a) Find the probability that the outcome 1 is first observed after
5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are
both observed.
(c) Find the expected number of rolls until the outcome 3 is
observed three times.
(d) Find the probability that the outcome 3 is observed exactly
three times in 10 rolls
given that it is first observed...

Assume we roll a fair four-sided die marked with 1, 2, 3 and
4.
(a) Find the probability that the outcome 1 is first observed after
5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are
both observed.
(c) Find the expected number of rolls until the outcome 3 is
observed three times.
(d) Find the probability that the outcome 3 is observed exactly
three times in 10 rolls
given that it is first observed...

if you roll a fair die 7 times, find the probability that you
never roll a number smaller than 6

Howard rolls a fair, 6 sided die 6 times. He is recording how
many times he rolls a multiple of 3. What is the probability of
Howard rolling exactly 3 multiples of 3? Show your work.

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