CareerCup

The result has NO related with the color of car and the music of listening. The only thing which will effects the result is date.

So John will have 30% probability reaching office before the time on Tuesday and Friday.

The answer should be c). It is not reasonable to expect a causal relationship between color of car, music, and the time arrived at work.

I think the option (a would maximize his chance
because,
for option (a
prob(driving red car AND listening to POP music AND arriving earlier on Friday) =
0.4*0.4*0.3 = 4.8%
for option (b
= 0.3 * 0.3 * 0.3 = 2.7%

a.) would maximize his chances to reach office early
Total cases=10
a.)probability=probability of driving red car *probability of listening to POP music * probability of reaching office early on friday = 4/10 * 4/10 * 3/10=0.048
b.)probability=probability of driving blue car *probability of listening to rock music * probability of reaching office early on teusday= 3/10 * 3/10 * 3/10=0.027

Probability for option a = 0.4+0.4+0.3 = 1.1
Probability for option b = 0.3+0.3+0.3 = 0.9

Ideal total probability = ideal option a probability + ideal option b probability = 1+1 = 2
obtained probability = option a probability + option b probability = 1.1+0.9=2

Percentage probability:
Option a percentage = 1.1/2 = 55%
Option b percentage = 0.9/2 = 45%

So option a is optimal with 55% probability

prob of option a =.4*.4*.3=.048
prob of option b=.3*.3*.3=.027

probability of option a is .4*.4*.3=0.048
probability of option b is .3*.3*.3=0.027
as all these are independent events.so option a has more probability

Answer is B

a) .4*.4*.3 = 0.048
b) .3*.3*.3 = 0.027

a).4*.4*.6=.096
b).3*.3*.6=.042

as he has to go either on tuesday or friday

I thinks both of question are "whatever" because the color of car and music type do not related with the result.

Based on observation, we got 30% probability to reaching at office before the time. So whatever the color of car which John drives or whatever the music John listening. John will has 30% probability to reaching at office on Friday and Tuesday.

I think (b) maximises his chance to reach office before the time. Because,

for (a), 4 are driving red car and listening pop music, but as he noticed just 3 of them reached office before time on Friday. So, the probability for him here can be 3/4, which is less than 1..!
for (b), 3 are driving blue car and listening rock music and reaching at office before the time on Tuesday. So, the probability for him in this scenario can be 3/3, which is 1!

Now you tell me which is better for him..! :-)