Question

two
dice are tossed; what is the probability that the numbers are the
same on both dice if it is known that the sum of the spots is
6

Answer #1

When two dice are tossed, then we get the sample space,

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1,(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6))}. So, n(S)=36

Let us define **an event A as
numbers are the same on both dice** i.e.,
A={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}. So, n(A)=6

Let us define **an event B as
sum of the spots is 6** i.e.
B={(1,5),(2,4),(3,3),(4,2),(5,1)}. So, n(B)=5

Thus, we have A⋂B={(3,3)}

P(A)=6/36=1/6, P(B)=5/36 and P(A⋂B)=1/36

We have to find the probability that the numbers are the same on both dice if it is known that the sum of the spots is 6 i.e. P(A|B)

By conditional probability, we can write,

**P(A|B)=(P(A⋂B))/P(B) =
(1/36)/(5/36) =1/5**

Two fair dice (6 sides) are tossed.
a) What is the probability that the sum of the tosses is 6 or 10
?
b) But what if it is given that the outcome of the first or the
second dice is 5 ?

A pair of dice is tossed twice. Find the probability that both
rolls give a sum of 6

A pair of dice is tossed twice.
Find the probability that both rolls give a sum of 6. (Enter your
probability as a fraction.)

Decide if events A and B are independent using
conditional probability.
(a) Two dice are tossed. Let A = “sum of 8”
and B = “both numbers are even.”
(b) Select a single card from a standard deck. Let
A = “a heart” and B = “an ace.”
(c) A couple have known blood genotypes AB
and BO. Let A = “their child has genotype
BO” and B = “their child has blood type
B.”

A pair of dice are tossed. What is the probability that doubles
are rolled, given that the sum on the two dice is less than 5?
(Round your answer to three decimal places.)

Two
dice are trown. What is the probability that the same number
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Three dice are rolled and two fair coins are tossed. Let X be
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If two fair dice are rolled, what is the probability that the
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Suppose you roll two dice (normal six sided dice). What is the
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Suppose you roll two dice (normal six sided dice). What is the
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8?

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