Carol is running on the cross-country team, and she's really good at that too! It is...

Carol is running on the cross-country team, and she's really good at that too! It is estimated that Carol has a 60% probability of winning any race that she enters. There are five races left this year.

1.) What is the probability that Carol wins all five races?

2.) Following the same assumptions, what is the probability that Carol loses all five races?

3.) Why don't the answers to the previous two problems add up to 100%?

4.) Finally, what is the probability that Carol wins at least one race?

Solutions

Expert Solution

probability of winning any race that she enters = p = 60% = 0.6

1.) What is the probability that Carol wins all five races?

P[ Carol wins all five races ] = p^5

P[ Carol wins all five races ] = 0.6^5

P[ Carol wins all five races ] = 0.07776

P[ Carol wins all five races ] = 7.776 %

2.) Following the same assumptions, what is the probability that Carol loses all five races?

P[ Carol loses all five races ] = ( 1 - p)^5

P[ Carol loses all five races ] = ( 1 - 0.6)^5

P[ Carol loses all five races ] = 0.4^5

P[ Carol loses all five races ] = 0.001024

P[ Carol loses all five races ] = 0.1024%

3.) Why don't the answers to the previous two problems add up to 100%?

because there are more cases of winning 1 , 2 or more races

4.) Finally, what is the probability that Carol wins at least one race?

P[ Carol wins at least one race ] = 1 - P[ Carol loses all five races ]

P[ Carol wins at least one race ] = 1 - 0.001024

P[ Carol wins at least one race ] = 0.998976

P[ Carol wins at least one race ] = 99.8976%

orchestra answered 1 year ago

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