Question

Problem 1 (2.5 points). What is the probability of drawing a 3-card hand (from a 52-card deck) containing cards of increasing consecutive ranks, where the first and the last card are of the same suite. For example, (3, 44, 5), (9, 10, J*), (10%, JY, Qa), (Q4, K, Ad). Use bijection to compute a number of favorable outcomes.

Answer 1

Solution increasi reasing consecutive All the different fferent three three rank combination aree 6, 7,5) 6,8,9) ,3,4) (3, 44.5) (4,5,6) ,6,) 5, 6, 5) (4.5, 8,9,10) cook, A) 09,10J) (10,30 (10,J,Q) (3,0, CO (J,o,k) last card should be the e first and from the can they same same su suite therefore be fill in 4 ways. The middle card can be freom so it can be fill by 4 ways. any suite The reeforce sequence total number of consecutive of ways in numbers which can be made is - 4x4 = 16 ways There are in total 1 sequence. So total number of favourable combination =16x11 = 176 Total number can be made of threee card using the 52 combination that cards = 52c3 x 13 = 132600 - required Probability a 176 132600 = 0'00133