Mathematics Questions & Answers - Free Online Practice

2,286.

Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other?

View answer & explanation

Correct answer is B

= $(n - 1)!$ ways.

= $(5 - 1)!$ ways

= 24 ways.

2,287.

The probability of an event P is $\frac{3}{4}$ while that of another event Q is $\frac{1}{6}$ . If the probability of both P and Q is $\frac{1}{2}$ . What is the probability of either P or Q.

$\frac{1}{96}$

$\frac{1}{8}$

$\frac{5}{6}$

$\frac{11}{12}$

View answer & explanation

Correct answer is D

Prob of P = $\frac{3}{4}$

Prob of Q = $\frac{1}{6}$

Prob of both P or Q = $\frac{3}{4} + \frac{1}{6} = \frac{11}{12}$

2,288.

Two perfect dice are thrown together, Determine the probability of obtaining a total score of 8

$\frac{1}{12}$

$\frac{5}{36}$

$\frac{1}{6}$

$\frac{7}{36}$

View answer & explanation

Correct answer is B

$\begin{array}{c|c} & & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline a & 1 & 1, 1 & 1, 2 & 1, 3 & 1, 4 & 1, 5 & 1, 6\\\hline & 2 & 1,1 & 2, 2 & 2, 3 & 2, 4 & 2, 5 & 2, 6 \\\hline B & 3 & 3, 1 & 3, 2 & 3, 3 & 3, 4 & 3, 5 & 3, 6\\\hline & 4 & 4 , 1 & 4, 2 & 4, 3 & 4, 4 & 4, 5 & 4, 6\\\hline Die & 5 & 5, 1 & 5, 2 & 5, 3 & 5, 4 & 5, 5 & 5, 6 \\\hline & 6 & 6, 1 & 6, 2 & 6, 3 & 6, 4 & 6, 5 & 6, 6\end{array}$

Probability of obtaining total score of 8 = $\frac{5}{36}$

2,289.

If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores

$\frac{2}{3}$

$\frac{2}{3}\sqrt{3}$

$\sqrt{\frac{2}{3}}$

$\sqrt{\frac{3}{2}}$

View answer & explanation

Correct answer is C

(x) = $\frac{5 + 6 + 7}{3}$

= $\frac{18}{3}$

= 6

$\begin{array}{c|c} scores(X) & \text{d = (x - x) deviation} & (deviation)^2\\\hline 5 & 5 - 6 & 1\\ 6 & 6 - 6 & 0 \\ 7 & 7 - 6 & 1\\ \hline & & 2\end{array}$

S.D $\sqrt{\frac{\sum d^2}{n}}$ where d = deviation = (x - x)

= $\sqrt{\frac{2}{3}}$