Beyond GMAT免费公开课 GWD数学难题解析11-20

myice

转自Robert征途空间http://forum.topway.org/sns/spac ... ;do=blog&id=950

Beyond GMAT免费公开课 GWD数学难题解析
主讲人：Robert

题号后面括号里面对应的是GWD31套，第一个数字是套题号，第二个数字是具体题号。


11.(12Q6)

A box contains 10 light bulbs, fewer than half of which are defective.  Two bulbs are to be drawn simultaneously from the box.  If n of the bulbs in box are defective, what is the value of n?

(1)   The probability that the two bulbs to be drawn will be defective is 1/15.

(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

用概率的定义去做。

C(2,x)/C(10,2)=1/15

X(10-x)/C(10,2)=7/15

(D)

myice

20.(29Q17)

In a box of 12 pens, a total of 3 are defective.  If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?



A.    1/6

B.     2/9

C.     6/11

D.    9/16

E.     3/4

C(9,2)/C(12,2)

(C)

myice

19.(26Q3)

A coin that is tossed will land heads or tails, and each outcome has equal probability.  What is the probability that the coin will land heads at least once on two tosses?



A.   1/4

B.   1/3

C.   1/2

D.   2/3

E.    3/4

独立事件。用减法做。

(E)

myice

18.(25Q6)

A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T id 0.06, what is the probability that the string of lightbulbs will fail during time period T?



   A.0.06

   B.(0.06)^10

   C.1-(0.06)^10

   D.(0.94)^10

   E.1-(0.94)^10

独立事件。用减法做。

(E)

myice

17.(24Q4)

A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?

A.1/7  B. ¼  C. 5/14  D. 11/28  E. 13/26

用减法去做。

1-C(6,2)/C(8,2)=13/28

(E)

myice

16.(21Q37)

A gumball dispenser has 24 gumballs, 12 white and 12 black, which are dispensed at random.  If the first 3 gumballs dispensed are black, what is the probability that the next gumball dispensed will be black?



A.    1/2

B.     1/3

C.     1/4

D.    3/7

E.     3/8

还剩21个gumballs，9个black,12个white

(D)

myice

15.(18Q33)

If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?

0.22

0.32

0.37

0.46

0.63

非独立事件问题。P(非A∩非B)=P(非A)+P(非B)-P(非A∪非B)

如果要求P(非A∩非B)最大，那么P(非A∪非B)取最小。P(非A)=0.46，P(非B)=0.32，最小是0.46，所以：

P(非A∩非B)=0.32+0.46-0.46=0.32

(B)

myice

14.(18Q32)

What is the probability that event E or event F or both will occur?

(1)     The probability that event E will occur is 0.6.

(2)     The probability that event F will occur is 0.4.

这类题现在考的很少了。一般来说，GMAT考独立事件。

当两个事件独立，满足P(A∩B)=P(A)P(B)

否则P(A∩B)=P(A|B)P(B)

(E)

myice

14.(18Q32)

What is the probability that event E or event F or both will occur?

(1)     The probability that event E will occur is 0.6.

(2)     The probability that event F will occur is 0.4.

这类题现在考的很少了。一般来说，GMAT考独立事件。

当两个事件独立，满足P(A∩B)=P(A)P(B)

否则P(A∩B)=P(A|B)P(B)

(E)

myice

13.(16Q27)

A box contains exactly 24 balls, of which 12 are red and 12 are blue.  If two balls are to be picked from this box at random and without replacement, what is the probability that both balls will be red?



A.    11/46

B.     1/4

C.     5/12

D.    17/40

E.     19/40

概率定义做。

C(12,2)/C(24,2)

(A)