A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis. What is the probability that all specimens of one of the two types of rock are selected for analysis?

The probability that all specimens of one of the two types of rock are selected for analysis is 0.0325

Step-by-step explanation:

Step 1

Given in the question that there are 10 specimens of basaltic rock and 10 specimens of granite.

The Total specimen sample collected =20

Step 2

The probability of selecting a basaltic rock is= 10 / 20 = 0.5

The probability of selecting a granite is= 10 / 20 = 0.5

So, the probability mass function of the number of basalt specimens selected for analysis is given by

Step 3

The probability that all specimens of one of the two types of rock are selected for analysis is given by the

sum of the probabilities that 10 basalt specimens and 5 igneous specimen is selected and the probabilities that 5 basalt specimens and 10 igneous specimen is selected.

The probability that 10 basalt specimens and 5 igneous specimen is selected is given by

The probability that 5 basalt specimens and 10 igneous specimen is selected is also given by

Therefore, the probability that all specimens of one of the two types of rock are selected for analysis is given by

Step 4

Multiplying 2 with the output

2(0.01625) = 0.0325

The probability that all specimens of one of the two types of rock are selected for analysis is 0.0325

b

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."