B

Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = [latex]\frac {8}{14}[/latex] = [latex]\frac {4}{7}[/latex].

A

Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = [latex]\frac {12}{52}[/latex] = [latex]\frac {3}{13}[/latex].

D

Let S be the sample space.
Then, n(S) = [latex]^{52}{C}_{2}[/latex] = [latex]\frac {(52 x 51)}{(2 x 1)}[/latex] = 1326.
Let E = event of getting 1 spade and 1 heart.
n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = [latex]^{13}{C}_{1} \times ^{13}{C}_{1} = 169[/latex].
P(E) = [latex]\frac {n(E)}{n(S)} = \frac {169}{1326} = \frac {13}{102}[/latex].

A

Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.
Then,E = [(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)]
n(E) = 14.
Hence, P(E) = [latex]\frac {n(E)}{n(S)} = \frac {14}{36} = \frac {7}{18}[/latex]

C

1 year = 365 days . A leap year has 366 days
A year has 52 weeks. Hence there will be 52 Sundays for sure.
52 weeks = 52 x 7 = 364 days
366 – 364 = 2 days
In a leap year there will be 52 Sundays and 2 days will be left.
These 2 days can be:
1. Sunday, Monday
2. Monday, Tuesday
3. Tuesday, Wednesday
4. Wednesday, Thursday
5. Thursday, Friday
6. Friday, Saturday
7. Saturday, Sunday
Of these total 7 outcomes, the favorable outcomes are 2.
Hence the probability of getting 53 days = [latex]\frac {2}{7}[/latex]