Question

In a bike showroom, there is a $60\%$ chance that a customer purchases a bike and ${\frac{1}{3}}^{rd}$ of those customers also purchase accessories. Using the simulator that generates random two digits numbers using digits from 1 through 5, work out the probability that the customer who enters the showroom purchases both bikes as well as the accessories.

32	43	32	42	55	52	33	22	53	21
13	43	54	25	54	14	31	44	45	34
53	24	21	51	32	25	11	45	51	41
54	12	35	31	32	54	55	24	37	12
33	50	34	44	21	23	55	34	41	12

• A. $30\%$
• B. $15$
• C. $10\%$
• D. $20\%$

Answer 1

The correct option is A $30\%$

There is a $60\%$ chance that a customer purchases the bike, and ${\frac{1}{3}}^{rd}$ out of those purchase accessories.
The simulator works with digits 1 to $5.60\%$ of 5 is 3 digits.
Let us take 1, 2, and 3 as bikes sold.
${\left(\frac{1}{3}\right)}^{rd}$out of those buy accessories, hence only 1 represents accessories that were purchased along with bikes.

Also,
Let the ones digit represent accessories brought and the tens place represent bikes purchased.

6 out of 50 fits the criteria, so

Expected probability $=\frac{6}{50}\times 100$

$=12\%$

The expected probability of a customer buying a bike as well as accessories is $12\%$.