When a red die and a blue die are rolled, the sample space consists of 36 elements. (a) Construct this sample space. (b) How many elements in the sample space exhibit a 6 on one or both dice? (c) How many elements in the sample space exhibit an even number (2, 4, 6) on the blue die?
1.When a red die and a blue die are rolled, the
(a) Construct this sample space.
(b) How many elements in the sample space
exhibit a 6 on one or both dice?
(c) How many elements in the sample space
exhibit an even number (2, 4, 6) on the
blue die?
(d) How many elements in the sample space
exhibits a 6 on either die (part b) and an
even number on the the blue die (part c)?
(e) Why doesn’t (b) and (c) add up to (d)?
2. Calculate the probabilities associated with
rolling 2 dice.
(a) Pr (rolling a sum of 7 on both dice)
(b) Pr (rolling a sum of 11)
(c) Pr (rolling a sum of 7 or 11)
3.Calculate the probabilities associated with
rolling 2 dice.
(a) Pr (rolling a 6 on the blue die)
(b) Pr (rolling a 6 on the red die)
(c) Pr (rolling only one 6)
(d) Why does your answers in (a) & (b) add
up to (c)?
4. Calculate the probabilities associated with
rolling 2 dice.
(a) Pr (rolling a 6 on the red die or a 6 on the
blue die) – only one 6
(b) Pr (rolling a 6 on the red die and a 6 on the
blue die) – both dice
(c) Pr (rolling at least one 6) – either die
(d) Why don’t your answers in (a) & (b) add
up to (c)?
5.Consider a standard deck of playing cards (52
cards). One card is drawn from the deck,
calculate the following probabilities.
(a) Pr (drawing an ace card)
(b) Pr (drawing a face card) – J, Q, K cards
(c) Pr (drawing an ace or a face card)
(d) Why does your answers in (a) & (b) add
up to (c)?
6. Consider a standard deck of playing cards (52
cards). One card is drawn from the deck,
calculate the following probabilities.
(a) Pr (drawing a red card)
(b) Pr (drawing a face card) – J, Q, K cards
(c) Pr (drawing a red or a face card)
(d) Why doesn’t your answers in (a) & (b) add
up to (c)?
7. Two dice are rolled. It is observed that the first
roll is a six (6).
(a) Determine the “reduced sample space”
(b) Calculate the probability of rolling a sum
of seven given that the first roll is a six
(c) Calculate the probability of rolling a pair
of sixes given that the first roll is a six
8. Two cards are dealt/drawn from a standard
deck of playing cards. Let A be the
where “an ace and a king are dealt”, B as the
event that “one card is a king”.
(a) Pr (A)
(b) Determine the “reduced sample space”
given that one of the cards is a king
(c) Pr (A | B)
where “an ace and a king are dealt”, B as the
event that “one card is a king”, C is the event
that “one card is a queen”.
(a) Pr (A | C)
(b) Pr (B | C)
selected at random.
(a) Pr (2nd is blue | 1st is blue)
(b) Pr (2nd is red | 1st is blue)
(c) Pr (2nd is white | 1st is blue)
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d) How many elements in the
exhibits a 6 on either die (part b) and an
even number on the the blue die (part c)?
(e) Why doesn’t (b) and (c) add up to (d)?
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