WAEC Past Questions and Answers - Page 1039

5,191.

A bag contains 5 red and 5 blue identical balls. Three balls are selected at random without replacement. Determine the probability of selecting balls alternating in color.

A.

\(\frac{7}{18}\)

B.

\(\frac{5}{18}\)

C.

\(\frac{5}{36}\)

D.

\(\frac{1}{36}\)

Correct answer is C

probability of selecting three balls with alternating colours = probability of selecting a blue ball (without replacement) x probability of selecting a red ball (without replacement) x probability of selecting a blue ball (without replacement)

In this case, we will be using the first instance (both would give the same answer since the number of blue and red balls are equal)

first: probability of selecting a red ball (without replacement) = \(\frac{5}{10}\) = \(\frac{1}{2}\)

second: the probability of selecting a blue ball (without replacement) = \(\frac{5}{9}\)

third: probability of selecting a red ball (without replacement) = \(\frac{4}{8}\) = \(\frac{1}{2}\)

Therefore, the probability of selecting three balls with alternating colours = \(\frac{1}{2}\) x \(\frac{5}{9}\) x \(\frac{1}{2}\)

= \(\frac{5}{36}\)

5,192.

The variables x and y are such that y =2x\(^3\) - 2x\(^2\) - 5x + 5. Calculate the corresponding change in y and x changes from 2.00 to 2.05.

A.

0.58

B.

0.95

C.

1.48

D.

1.95

Correct answer is A

When x = 2

y = 2(2)\(^3\) - 2(2)\(^2\) 

-5(2) + 5

y = 16 - 8 - 10 + 5

y = 3 

 

when x = 2.05 

y = 2(2.105)\(^3\) - 2(2.05)\(^2\)

- 5(2.05) + 5

y = 17.23 - 8.405 - 10.25 + 5

y = 3.575 - 3

Difference = 3.575 - 3

= 0.58

5,194.

Calculate the variance of \(\sqrt{2}\), (1 + \(\sqrt{2}\)) and (2 + \(\sqrt{2}\)) 

A.

0

B.

\(\sqrt{\frac{2}{3}}\)

C.

\(\frac{2}{3}\)

D.

2

Correct answer is C

x (x - \(\bar{x}\)) (x - \(\bar{x}\))

\(\sqrt{2}\)

1 + \(\sqrt{2}\)

2 + \(\sqrt{2}\) 

-1

0

1

1

0

1

\(\overline{2}\)

 

variance = \(\frac{\sum(x - \bar{x})^2}{n}\)

= \(\frac{2}{3}\) 

5,195.

A force of 230N acts in its direction 065\(^o\). Find its horizontal component.

A.

208.5N

B.

197.2N

C.

118.5N

D.

97.2

Correct answer is D

Horizontal component = 230 cos 64 

= 97.2N