JAMB Mathematics Past Questions & Answers - Page 332

1,656.

A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.

A.

\(\frac{3}{8}\)

B.

\(\frac{1}{3}\)

C.

\(\frac{7}{24}\)

D.

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

Correct answer is B

n(apples) = 9
n(bananas) = 8
n(oranges) = 7

n(\(\varepsilon\)) = 24

Hence Prob(not apple, nor orange) = Prob(banana) = \(\frac{8}{24}\) = \(\frac{1}{3}\)

1,657.

What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at random is divisible by both 2 and 3?

A.

\(\frac{1}{25}\)

B.

\(\frac{1}{5}\)

C.

\(\frac{4}{25}\)

D.

\(\frac{3}{4}\)

Correct answer is C

\((1 \leq x \leq 25)\) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}

Number N of x divisible by both 2 and 3 is 4.

n(\(\varepsilon\)) = 25

= \(\frac{N}{n(\varepsilon)}\)

= \(\frac{4}{25}\)

1,658.

In how many ways can 3 seats be occupied if 5 people are willing to sit?

A.

60

B.

20

C.

5

D.

120

Correct answer is A

5 people can take 3 places in;

5P3 ways, = \(\frac{5!}{(5 - 3)!}\) = \(\frac{5!}{2!}\)

= \(\frac{5 \times 4 \times 3 \times 2!}{2!}\)

= 5 x 4 x 3

= 60 ways

1,659.

In how many ways can a student select 2 subjects from 5 subjects?

A.

\(\frac{5!}{3!}\)

B.

\(\frac{5!}{2!2!}\)

C.

\(\frac{5!}{2!3!}\)

D.

\(\frac{5!}{2!}\)

Correct answer is C

A student can select 2 subjects from 5 subjects in;

5C3 ways, i.e. = \(\frac{5!}{2!(5 - 2)!}\)

= \(\frac{5!}{2!3!}\)