Answer: 3/13

Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52 = 3/13 .

Answer: 2/91

Explanation:

Answer: 2/7

Explanation:
P (getting a prize) = 10/(10 + 25) = 10/35 = 2/7 
    

Answer: 1/3

Explanation:

Answer: 8/35 

Explanation:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35

Answer: 9/25

Explanation:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25

Answer: ⁶C₃ / ¹⁰C₃

Explanation:
The basket contains 6 good and 9 rotten fruits.
=> P(drawing 3 good fruits) = ⁶C₃/ ¹⁰C₃

Answer: 103/105

Explanation:
 Given P(A) = 2/3, P(B) = 5/7 and P(C) = 4/5
=> Probability of problem being solved
=> P(A U B U C) = 1 – (A ᴖ B ᴖ C)
=> 1 – P(A), P(B) P(C)
=> = 1 P(A dash) P(B dash) P(C dash)
=> = 1 – 1/3(2/7)(1/5) = 1 – 2/105
P(A U B U C) = 103/105

Answer: 9/13

Explanation:
A card can be drawn from a pack of cards in 52C1 ways i.e, n(S) = 52
=> There are 36 numbered cards, of which one card can be drawn in
=> 36C1 ways, i.e., n(E) = 36.

Answer: 210 – 1 / 210

Explanation:
Let E be the event of heads occurring at least once and E- be the event of heads not occurring at all i.e. all tails.
=> P(E) = 1 – P(E dash)
=> 1 – ½10 = 210 – 1 / 210