13 What is the probability that the first card is an ace and the second card is

Question

13 What is the probability that the first card is an ace and the second card is a heart? b. What is the probability that the fist card is a king or the second cardis a club? 8. An urn contains 3 red and 5 yellow balls. Two balls are sélected without replacement. What is the probability that a. The first ball is red and the second is yellow? b. S z 196 ysl 1 . 56 · Both balls are red? : % c. At least one of the balls is yellow? 9. Every Wayne State student has an access id; the 6character name consisting of 2 letters (a-z) followed by 4 numbers (0-9) a. How many access ids are possible? 676opo0 52%000 o b. How many access ids are possible if letters and numbers cannot be repeated? 10. A statistics class has 24 students where students work in groups of 4 every week that are randomly assigned. a. What is the probability a student will work in the same group of 4 this week that they did Y10624 last week? If the class has 14 females and 10 males, how many groups can be made that have 2 males b. o45 and 2 females?

Explanation / Answer

7)a) P(first is ace and second is heart) = 4/52 * 13/52 = 0.029

B) P(first is king or second is club) = P(first is king) + P(second is club) - P(first is king and second is club)

= 4/52 + 13/52 - 1/52 = 16/52 = 0.31

8) a) P(first is red and second is yellow) = 3/8 * 5/7 = 15/56 = 0.27

B) (both balls are red) = 3C2/8C2 = 0.107

C) P(at least one is yellow) = (5C1 * 3C1 + 5C2)/8C2 = 0.89

9)a) No of access IDs are possible =( 26)2 * (10)4 = 6760000

B) No of access IDs are possible if letter and number are not repeated = 26P2 * 10P4 = 3276000

10)a) Probability = 1/24C4 = 1/10626

B) no of groups = 14C2 * 10C2 = 4095

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