Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.

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Question:

Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.

Find the probability:

The probability that Joshua beats Eric in ping pong AND pool?

The probability that Joshua beats Eric in ping pong OR pool?

P(pp & pool) = 22%

There is 22% probability that Joshua beats Eric in ping pong AND pool.

P(pp OR pool) = 50%

There is 50% probability that Joshua beats Eric in ping pong OR pool.

Step-by-step explanation:

The probability Joshua beats Eric in ping pong is given by

P(pp) = 0.48

The probability Joshua beats Eric in pool is given by

P(pool) = 0.46

The probability that Joshua beats Eric in ping pong AND pool is given by

P(pp & pool) = P(pp)×P(pool)

P(pp & pool) = 0.48×0.46

P(pp & pool) = 0.22

P(pp & pool) = 22%

Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.

The probability that Joshua beats Eric in ping pong OR pool is given by

P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54

Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)

Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)

P(pp OR pool) = 0.48×0.52 + 0.46×0.54

P(pp OR pool) = 0.25 + 0.25

P(pp OR pool) = 0.50

P(pp OR pool) = 50%

Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.

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