Rhonda is playing a board game. The players take turns rolling a pair of number cubes. On her next turn Rhonda must roll a 5 to win the game, but if she rolls a double she gets an extra turn.

a. Explain why the events Rolling a 5 and Rolling Doubles are mutually exclusive.

b. If the probability of rolling a 5 is 1/9 and the probability of rolling doubles is 1/6, what is the probability that Rhonda rolls either a 5 or doubles on her next turn. Express your answer as a fraction in simplest form.

Question

Mathematics

Adriel Ruiz

17 June, 01:29

Rhonda is playing a board game. The players take turns rolling a pair of number cubes. On her next turn Rhonda must roll a 5 to win the game, but if she rolls a double she gets an extra turn.

a. Explain why the events Rolling a 5 and Rolling Doubles are mutually exclusive.

b. If the probability of rolling a 5 is 1/9 and the probability of rolling doubles is 1/6, what is the probability that Rhonda rolls either a 5 or doubles on her next turn. Express your answer as a fraction in simplest form.

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Answers (1)

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Nikolai Haley · Answer 1

A) We presume "roll a 5" means rolling the dice so they come up with a total of 5 spots on top. 5 is not an even number, so when 5 is showing, the numbers on the two dice must be different, hence cannot be doubles.

b) Since these events are mutually exclusive, we can simply add their probabilities: (1/9) + (1/6) = 2/18 + 3/18 = 5/18.