2 numbered cards are picked randomly from a complete set of Heart and Club cards (26 cards), find the probability that the sum of numbers on card is a perfect square number?
1. 13/1326
2. 14/325
3. 11/1326
4. 4/112
5. 5/789
2 numbered cards are picked randomly from a complete set of Heart and Club cards (26 cards), find the probability that the sum of numbers on card is a perfect square number?
1. 13/1326
2. 14/325
3. 11/1326
4. 4/112
5. 5/789
1. 13/1326
2. 14/325
3. 11/1326
4. 4/112
5. 5/789
Correct Answer – Option 2 : 14/325
Given:
2 cards are picked randomly from 26 cards
Formula Used:
The number of ways of picking “r” cards from “n” total cards = nCr
Calculation:
Total numberd card in a pack of deck (2 – 10) = 9 × 2 = 18
Perfect squares that can be obtained by sum of numbers in a deck = 4, 9, 16
Sum of numbers on cards possible to get 4 = {(1,3) (2,2) (3,1)} = 3
Sum of numbers on cards possible to get 9 = {(2,7) (3,6) (4,5) (5,4) (6,3) (7,2)} = 6
Sum of numbers on cards possible to get 16 = {(6,10) (7,9) (9,7) (10,6) (8,8)} = 5
Number of favorable outcomes = 3 + 6 + 5 = 14
Total number of favorable outcomes = 26C2 = (26 × 25)/(2 × 1) = 325
∴ P(A) = 14/325
∴ The probability that the sum of numbers on card is a perfect square number is 14/325