The probability that Babe Ruth hits a home run on any given at-bat is 0.12, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)

A) 0.072 = 7.2%

B) 8.3333 at-bats (8 to 9 at-bats)

Step-by-step explanation:

A)

If the chance of hitting a home run is 0.12, the chance of not hitting a home run is 1 - 0.12 = 0.88.

To find the probability of the next home run being in the fifth strike, we need the four other strikes to not be a home run, so the probability is:

P = (0.88)^4 * 0.12 = 0.072 = 7.2%

B)

To find the expected number of at-bats until the next home run, we just need to divide 100% by the probability of hitting a home run (0.12 = 12%):

100/12 = 8.3333

So the expected number is 8 to 9 at-bats

7

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is