A game is played where two unbiased dice are rolled and the score in the gal greater of the two numbers shown. If the two numbers are the same, then the score in the game is the number shown on one of the dice. A diagram showing the possible outcomes is given below. First die 3. 4. 2.

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Chapter1: Combinatorial Analysis
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A game is played where two unbiased dice are rolled and the score in the game is the
greater of the two numbers shown. If the two numbers are the same, then the score in the
game is the number shown on one of the dice. A diagram showing the possible outcomes is
given below.
First die
3.
4.
6.
Let T be the random variable "the score in a game".
(a)
Complete the table to show the probability distribution of T.
1
3
4.
6.
P(T=1)
(b)
Find the probability that
(i)
a player scores at least 3 in a game.
(ii)
a player scores 6, given that they scored at least 3.
(c)
Find the expected score of a game.
3.
4.
Second die
Transcribed Image Text:A game is played where two unbiased dice are rolled and the score in the game is the greater of the two numbers shown. If the two numbers are the same, then the score in the game is the number shown on one of the dice. A diagram showing the possible outcomes is given below. First die 3. 4. 6. Let T be the random variable "the score in a game". (a) Complete the table to show the probability distribution of T. 1 3 4. 6. P(T=1) (b) Find the probability that (i) a player scores at least 3 in a game. (ii) a player scores 6, given that they scored at least 3. (c) Find the expected score of a game. 3. 4. Second die
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