Question

In: Statistics and Probability

Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. What...

Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. What is the probability that the number will be more than 5 or odd? (Enter your probability as a fraction.)

Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number.)

rolling a 4 or doubles

Use the data in the table below, which shows the employment status of individuals in a particular town by age group.

Age Full-time Part-time Unemployed
0—17 27 170 358
18—25 199 199 272
26—34 342 71 22
35—49 521 175 238
50+ 350 165 303

If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?

Solutions

Expert Solution

Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive. What is the probability that the number will be more than 5 or odd? (Enter your probability as a fraction.)

We have 5 numbers(6,7,8,9,10) above 5 and 5 odd numbers(1,3,5,7,9) in ten numbers. The common numbers in these two are 7 and 9. So the probability that the number will be more than 5 or odd is

P(x>5 U x is odd)= P(x>5) +p(x is odd) -p(x>5 x is odd)

=5/10+5/10-2/10

=4/5

​

Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number.)

rolling a 4 or doubles

Probability of rolling a sum of 4 =3/36=1/12

Probability of both die showing the same number is =6/36=1/6

Sum of two variables
y
x 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

The common numbers in these two is one.

Probability of rolling a 4 or doubles= 3/36+6/36-1/36=2/9

​

If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?

Age Full-time Part-time Unemployed Total
0—17 27 170 358 555
18—25 199 199 272 670
26—34 342 71 22 435
35—49 521 175 238 934
50+ 350 165 303 818
Total 1439 780 1193 3412

The probability that the person is under 18 =555/3412

The probability that the person employed part-time= 780/3412

The common numbers in these two is that the person is under 18 and employed part-time=170/3412

P(x<18 U x is employed part-time)= P(x<18 +p(x is employed part-time) -p(x<18 x is employed part-time)

=555/3412+780/3412-170/3412=

1165/3412​

orchestra answered 3 years ago
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