6. When a die (one of a pair of dice) is rolled, it has an equal probability of

Question

6. When a die (one of a pair of dice) is rolled, it has an equal probability of landing on any of its six sides.

a. What is the probability of rolling a 3 with a single throw?

b. When a die is rolled twice, what is the probability that only one of the throws will be a 3?

c. When a die is rolled twice, what is the probability that at least one of the throws will be a 3?

d. When a die is rolled twice, what is the probability that the first throw will be a 3 and the second will be a 6?

e. When a die is rolled twice, what is the probability that one throw will result in a 3 and the other throw will result in a 6?

f. If two dice are rolled together, what is the combined probability that one will be a 3 and the other will be a 6?

g. If one die is rolled and it comes up as an odd number, what is the probability that it is a 5?

h. If two dice are rolled together, what is the probability that the sum of the two dice will add up to 7?

i. If a die is rolled 6 times, what is the probability that at least one of the throws is a 3?

Explanation / Answer

a)probability of rolling a 3 with a single throw =(1/6) (as there are six outcomes of which 3 is one)

b)

probability that only one of the throws will be a 3=P(first is 3 and seconnd one none+first not 3 and second is 3)

=(1/6)*(5/6)+(5/6)*(1/6) =10/36 =5/18

c) e probability that at least one of the throws will be a 3=1-P(none is 3) =1-(5/6)*(5/6)=11/36

d)probability that the first throw will be a 3 and the second will be a 6=(1/6)*(1/6) =1/36

e) probability that one throw will result in a 3 and the other throw will result in a 6=P(first 3 and second 6+first 6 and second 3) =(1/6)*(1/6)+(1/6)*(1/6) =2/36 =1/18

f) combined probability that one will be a 3 and the other will be a 6 =2/36 =1/18

g)

P(5 if odd) =1/3 (as there are 3 odd numbers out of whcih one s 5)

h) P(S=7) =6/36 =1/6 (as 6 event out of 36 where sum can be 7)

i) P(at least one of the throws is a 3) =1-P(nne of die shows 3) =1-(5/6)6 =0.6651

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