1) A pair of dice (one red and one blue) are thrown. Each die has six sides. The

Question

1) A pair of dice (one red and one blue) are thrown. Each die has six sides. The dice are fair, so each outcome is equally likely. What is the probability that the number that comes up on the blue die is one more than the number on the red die?

2) Three different colored dice (red, blue, and green) are thrown. Each die has six sides. The dice are fair so each outcome is equally likely. What is the probability that at least one of the die comes up 6?

3)10 kids are randomly grouped into an A team with five kids and a B team with five kids. Each grouping is equally likely.

(a)What is the size of the sample space?

(b)There are two kids in the group, Alex and his best friend Jose. What is the probability that Alex and Jose end up on the same team?

(c)If the group consists of five girls and five boys, what is the probability that all the girls end up on the same team?

PLEASE ONLY ANSWER IF YOU CAN DO ALLLLL OF THEM!

Explanation / Answer

A) total outcomes are 36

Favourable outcones are (1,2),(2,3),(3,4),(4,5),(5,6)

So probability is 5 /36.

B) total outcomes = 216

Favourable outcomes are 91 .

Hence probability is 91/216

C) 1) as there are two teams and 10 people . So number of possible outcomes is 2^10 = 1024.

So size of sample space is 1024 elements.

2) As Alex and Jose want to be in same team . So the possibility is (5!/3!)×(5!/3!) = 5×4 ×5×4 = 400

So probability of them to be in same team is 400/1024.

3) probability that all the girls end up on the same team is (5!/0!)×(5!/0!) = 1

Hence the probability of it is 1/1024

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