Question

Dan either walks or cycles to school. The probability that he cycles to school is $\dfrac{1}{3}$
A.Write down the probability that Dan walks to school.
B.There are 198days in a school year. Work out the expected number of days that Dan cycles to school in a school year.

Answer 1

The question is related to probability. We will use the formula of probability that is ${\text{probability of event to happen}}P(E) = \dfrac{\text{number of favourable outcomes}}{\text{total number of outcome}}$. The total probability of any event is always 1.

Complete step-by-step answer:
We have two condition in the question that is
Dan either walks or cycles to school and the probability that Dan cycles to school is $\dfrac{1}{3}$
We know that the total probability of any event is = 1
So, the probability that Dan walks to school is = total probability – probability that Dan cycles to school
= $1 - \dfrac{1}{3}$
Do the L.C.M
$= \dfrac{{3 - 1}}{3}$
Solve the above equation
$= \dfrac{2}{3}$
Hence the probability of Dan walks to school is $\dfrac{2}{3}$
(ii) Expected number of days that Dan cycles to school
${\text{expected number of days that Dan cycles to school in a school year}} = {\text{total number of days}} \times {\text{probability that Dan cycles to school}}$
$= 198 \times \dfrac{1}{3}$
Multiply and divide the above equation we get
$= \dfrac{198}{3}$
$= 66$
Expected number of days is 66 days.

Note: If P is the probability of an event to occur then then the probability of that event to not occur is 1-P. The sum of probabilities of a particular event to occur and not occur is always equal to 1.