A statistics practitioner determined that if a batter hits a line drive, the probability of an out is 23%. Determine the probability that in a game with 25 line drives, there
are 1 outs or more

There are 10-line drivers, n = 10.

The probability of success = p = 0.23.

The probability that there are at least 5 outs is:

P

(

X

≥

5

)

=

1

−

P

(

X

<

5

)

=

1

−

P

(

X

=

0

)

−

P

(

X

=

1

)

−

P

(

X

=

2

)

−

P

(

X

=

3

)

−

P

(

X

=

4

)

=

1

−

(

10

C

0

(

0.23

)

0

(

1

−

0.23

)

10

)

−

(

10

C

1

(

0.23

)

1

(

1

−

0.23

)

9

)

−

(

10

C

2

(

0.23

)

2

(

1

−

0.23

)

8

)

−

(

10

C

3

(

0.23

)

3

(

1

−

0.23

)

7

)

−

(

10

C

4

(

0.23

)

4

(

1

−

0.23

)

6

)

=

1

−

(

10

C

0

(

0.23

)

0

(

0.77

)

10

)

−

(

10

C

1

(

0.23

)

1

(

0.77

)

9

)

−

(

10

C

2

(

0.23

)

2

(

0.77

)

8

)

−

(

10

C

3

(

0.23

)

3

(

0.77

)

7

)

−

(

10

C

4

(

0.23

)

4

(

0.77

)

6

)

=

1

−

0.07326

−

0.2188

−

0.2942

−

0.2343

−

0.1224

=

1

−

0.94296

=

0.05704

536

step-by-step explanation: