May I ask you please some help in this two questions:

[ciurban]

May I ask you please some help in this two questions:

1. On any given day in Alamo City, the probability of a traffic jam occurring is 0.3, and the probability of heavy fog occurring is 0.5. If the probability that there is neither a traffic jam nor heavy fog is 0.4, then what is the probability that there is both a traffic jam and heavy fog?

0.15
0.4
0.8
0.2

2. A factory that manufactures tennis balls is expanding its production capacity. As production capacity expands, engineers calculate that the factory will have the following capacity(C) as a function of days (D) of expansion:
C = [1/3] * [(D/2) + 3]^3

How quickly is the rate of change in capacity increasing on the sixth day of expansion (in units of C/D^2) ?

12
72
22.37
81


Thank you very very much!

[Dblooos]

1. On any given day in Alamo City, the probability of a traffic jam occurring is 0.3, and the probability of heavy fog occurring is 0.5. If the probability that there is neither a traffic jam nor heavy fog is 0.4, then what is the probability that there is both a traffic jam and heavy fog?

0.15
0.4
0.8
0.2

We can solve this question with Venn diagram:

As we know that probability of all the event together is always 1.

So let us assume that probability of Traffic Jam and Heavy fog = x
Given:
Probability of Traffic Jam = 0.3-x
Probability of Heavy Fog = 0.5-x
Probability of neither traffic jam and heavy fog = 0.4

Adding all should be equal to 1

0.3-x + x + 0.5-x + 0.4 = 1
x= 1.2-1.0
x= 0.2

So probability of both traffic jam and heavy fog = 0.2

[Dblooos]

Experts, can you please provide help with the second question. I kind of didn't understand it too.

[theCodeToGMAT]

2. A factory that manufactures tennis balls is expanding its production capacity. As production capacity expands, engineers calculate that the factory will have the following capacity(C) as a function of days (D) of expansion:
C = 1/3 (D/2 + 3)^3

How quickly is the rate of change in capacity increasing on the sixth day of expansion (in units of C/D^2) ?

12
72
22.37
81

Do you mean

C = 1/[3*(D/2 + 3)^3]
or,
C = [1/3]*(D/2 + 3)^3

[ciurban]

The question says:

C = [1/3] * [(D/2) + 3]^3

Thank you in advance

2. A factory that manufactures tennis balls is expanding its production capacity. As production capacity expands, engineers calculate that the factory will have the following capacity(C) as a function of days (D) of expansion:
C = 1/3 (D/2 + 3)^3

How quickly is the rate of change in capacity increasing on the sixth day of expansion (in units of C/D^2) ?

12
72
22.37
81

Do you mean

C = 1/[3*(D/2 + 3)^3]
or,
C = [1/3]*(D/2 + 3)^3