Solution : The outcomes of the rolling of a pair of dice can be more readily understood by assigning
colors to the dice (e.g ., one red , one green ). An outcome of throwing aa pair of dice can be
represented by an ordered pair , where the first element is the side of the red die fecing up,
and the second is the side of the green die fecing up . Thus , (32) signifies a 3 on the red die
and a 2 on the green, while (23) signifies 2 on the red 3 on the green . Since there are ltbr. six feces on each die , there are ` 6xx6 = 36` possible outcomes in the same space . the
outcomes that have a sum of 7 are (61). (16), (52) , (25) , (43) and (34) . Therefore , the
probability of getting a sum of 7 is `(6)/(36) = (1)/(6)`
Probability questions can also be asked about two events A and B . Questions on the Math
Leval 2 Test cover the following three ways of combining two events
`*P(A cupB)` , the probability of either A or B occurring . where ` A cup B ` is called the disjunction
of A and B
` * (PA|B)` , the probability of A occurring , givne that B has occurred . This is called conditional
Probability
` * P(A nn B)` , the probabilty of both A and B occurring , where ` A nn B ` is called the conjunction
of A and B
If two event have no outcomes in common , they are called mutually exclusive , and `P(A uu B) = `
P(A) + P(B) . If two event no outcomes in common , these outcomes would be double counted ,
resulting i the more general formaula ` P(AuuB)= P(A) + P(A) - P(AnnB) ` . Note that A and B are
mutually exclusive if and only if ` P(A nn B ) = 0 ` .
What is the probability of getting a sum 7 when two dice are thrown?
∴ The probability of getting sum as 7 when two dice are thrown is 1/6.
What is the probability of getting a 7?
Possible outcomes on a single roll of a die are 1, 2, 3, 4, 5 and 6. Therefore, the chance of getting a 7 (favourable outcome) on rolling the die once is 0. Thus, the probability of the event is 0 or it is an impossible event.
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