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algol [13]
2 years ago
13

Colton has a 1/20 probability of winning the race. Logan has a 15% probability of winning. Who has the greater chance of winning

?
A Colton
B Logan
C They have an equal chance
Mathematics
1 answer:
LiRa [457]2 years ago
4 0

Answer:

Logan has the greater probability of winning

Step-by-step explanation:

Colton=1/20

=0.05

So the probability of Colton is 0.05

Logan=15%

=15/100

=0.15

So the probability of Logan is 0.15

When comparing the two,it was observed that the Logan has greater probability of winning

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a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

A = a + (A \cap B)

In which a is the probability that he wins the first race but not the second and A \cap B is the probability that he wins both these races.

By the same logic, we have that:

B = b + (A \cap B)

The probability that he wins both races is 0.5.

This means that A \cap B = 0.5

The probability that he wins the second race is 0.6

This means that B = 0.6

B = b + (A \cap B)

0.6 = b + 0.5

b = 0.1

The probability that he wins the first race is 0.7.

This means that A = 0.6

A = a + (A \cap B)

0.7 = a + 0.5

a = 0.2

A) he wins at least one race.

This is

P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

P = a + b = 0.2 + 0.1 = 0.3

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

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