Probability quiz 1

Explanations Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT] Total number of ways = 2 × 2 × 2 = 8.  Fav. Cases = 7 P (A) = 7/8 OR P (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8

Explanations Total Cards = 52. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) 9 from each suit 4 × 9 = 36 P (E) = 36/52 = 9/13

Explanations P (G) × P (R) = (5/12) x (7/11) = 35/132

Explanations Probability math - Total number of ways = 6 × 6 = 36 ways. Favorable cases = (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) --- 6 ways. P (A) = 6/36 = 1/6

Explanations

i) honor cards = (A, J, Q, K) 4 cards from each suits = 4 × 4 = 16 P (honor card) = 16/52 = 4/13

(ii) face cards = (J,Q,K) 3 cards from each suit = 3 × 4 = 12 Cards. P (face Card) = 12/52 = 3/13

Explanations Total number of ways = 6⁴ = 1296. Number of ways of getting a sum 22 are 6,6,6,4 = 4! / 3! = 4 6,6,5,5 = 4! / 2!2! = 6. Number of ways of getting a sum 23 is 6,6,6,5 = 4! / 3! = 4. Number of ways of getting a sum 24 is 6,6,6,6 = 1. Fav. Number of cases = 4 + 6 + 4 + 1 = 15 ways. P (getting a sum of 22 or more) = 15/1296 = 5/432

Explanations

Total number of cases = 6² = 36

Since the number on a die should be multiple of the other, the possibilities are (1, 1) (2, 2) (3, 3) ------ (6, 6) --- 6 ways

(2, 1) (1, 2) (1, 4) (4, 1) (1, 3) (3, 1) (1, 5) (5, 1) (6, 1) (1, 6) --- 10 ways

(2, 4) (4, 2) (2, 6) (6, 2) (3, 6) (6, 3) -- 6 ways

Favorable cases are = 6 + 10 + 6 = 22.

So, P (A) = 22/36 = 11/18

Explanations 15 persons can be seated in 14! Ways. No. of ways in which two particular people sit together is 13! × 2! The probability of two particular persons sitting together 13!2! / 14! = 1/7 Odds against the event = 6 : 1

Explanations A leap year can have 52 Sundays or 53 Sundays. In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days. Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed) (Wed, Thur) (Thur, Friday) (Friday, Sat). So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two favorable cases. So,  P (53 Sundays) = 2 / 7 Now, P(52 Sundays) + P(53 Sundays) = 1 So, P (52 Sundays) = 1 - P(53 Sundays) = 1 – (2/7) = (5/7)