Name: Probability: Expected Value of an Experiment
Uploaded: 2019-07-19
Duration: 5 min 11 s
Description: What is the average value of a random variable over a number of experiments, known as a mathematical expectation in probability theory? How do we calculate i...

Question

Two dice are rolled simultaneously and counts are added complete the table given below:

Event : 'Sum on $2$ dice'	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Probability	$\frac{1}{36}$						$\frac{1}{36}$				$\frac{1}{36}$

A student argues that 'there are $11$ possible outcomes $2, 3, 4, 5, 6, 7, 8, 9, 10, 11$ and
$12$ . Therefore, each of them has a probability $\frac{1}{11}$ . Do you agree with this argument? Justify your answer.

Accepted Answer

When two dices are rolled.
$\Rightarrow$ Number of total outcomes $= 6 \times 6 = 36$
$3$ Probability $= \frac{number of favourable outcome}{total outcome}$

Sum
on $2$
Dice Favourable outcome Number
of
favourable
outcome Probability

$2$ $(1, 1)$ $1$ $\frac{1}{36}$

$3$ $(1, 2) (2, 1)$ $2$ $\frac{2}{36}$

$4$ $(2, 2) (1, 3) (3, 1)$ $3$ $\frac{3}{36}$

$5$ $(2, 3) (3, 2) (4, 1) (1, 4)$ $4$ $\frac{4}{36}$

$6$ $\begin{array}{l} (2, 4) (4, 2) (5, 1) (1, 5) (3, 3) \end{array}$ $5$ $\frac{5}{36}$

$7$ $\begin{array}{l} (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) \end{array}$ $6$ $\frac{6}{36}$

$8$ $(2, 6) (6, 2) (3, 5) (5, 3) (4, 4)$ $5$ $\frac{5}{36}$

$9$ $(3, 6) (6, 3) (4, 5) (5, 4)$ $4$ $\frac{4}{36}$

$10$ $\begin{array}{l} (4, 6) (6, 4) (5, 5) \end{array}$ $3$ $\frac{3}{36}$

$11$ $(5, 6) (6, 5)$ $2$ $\frac{2}{36}$

$12$ $(6, 6)$ $1$ $\frac{1}{36}$

$\Rightarrow$ Complete table will be -

Event : 'Sum on $2$ dice' $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$

Probability $\frac{1}{36}$ $\frac{2}{36}$ $\frac{3}{36}$ $\frac{4}{36}$ $\frac{5}{36}$ $\frac{6}{36}$ $\frac{5}{36}$ $\frac{4}{36}$ $\frac{3}{36}$ $\frac{2}{36}$ $\frac{1}{36}$

Not every outcome has probability of $\frac{1}{11}$ . We do not agree with this argument because there are a different number of possible outcomes for each sum. According to the above table, we can see that each sum has different probability.

Important Questions on Probability

Learn and Prepare for any exam you want !

Event : 'Sum on $2$ dice'	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$9$	$(3, 6) (6, 3) (4, 5) (5, 4)$	$12$
Probability	$\frac{1}{36}$						$\frac{1}{36}$				$\frac{1}{36}$