SOLUTION: Suppose that you are performing the probability experiment of rolling one fair six-sided die. Let F be the event of rolling a four or a five. You are interested in how many times y
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Question 1206756: Suppose that you are performing the probability experiment of rolling one fair six-sided die. Let F be the event of rolling a four or a five. You are interested in how many times you need to roll the die in order to obtain the first four or five as the outcome.
• p = probability of success (event F occurs)
• q = probability of failure (event F does not occur)
Find the values of p and q. (Enter exact numbers as integers, fractions, or decimals.)
Find the probability that the first occurrence of event F (rolling a four or five) is on the second trial. (Round your answer to four decimal places.) Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website! .
Suppose that you are performing the probability experiment of rolling one fair six-sided die.
Let F be the event of rolling a four or a five. You are interested in how many times you need
to roll the die in order to obtain the first four or five as the outcome.
• p = probability of success (event F occurs)
• q = probability of failure (event F does not occur)
(a) Find the values of p and q. (Enter exact numbers as integers, fractions, or decimals.)
(b) Find the probability that the first occurrence of event F (rolling a four or five)
is on the second trial. (Round your answer to four decimal places.)
~~~~~~~~~~~~~~~~~~~~~~~~~
(a) p = probability that " a four or a five" occurs (event F). This probability is
p = + = = .
q = probability that event F does not occur. It is a complementary event to F.
q = 1 - p = 1 - = .
(b) Probability of (b) is
P = P(event F is not a first roll; event F is the second roll) = (1-p)*p = q*p = = .
