1. A classroom has 30 students, what is the probability that two students were b
ID: 3355454 • Letter: 1
Question
1. A classroom has 30 students, what is the probability that two students were born on the same day? Assume that birth dates are equally likely to occur any day of the year. 2. In poker, a royal flush is a hand that contains [A, K, Q,J, 10} all of the same suit. What is the probability of drawing a royal flush? 3. In poker, a full house is a hand that contains two matching cards of one rank and three matching cards of a different rank. For example, the hand {2H, 2S, 9S, 9H, 9C] is a full house. What is the probability of drawing a full house? 4. A test is given to a student that consists of 10 true/false questions. Suppose that in order to pass the test the student must score a 60% or higher. What is the chance that the student will I fe tdmaners for ach questin? 5. Traffic on highway 64 during rush hour travels at 70 miles/hour. The Missouri Department of Transportation puts in a sensor to detect when a car passes a specific point and determines that the average rate at which cars pass that point is 3 cars/sec during rush hour. What is the probability that a stretch of one mile of the highway contains exactly 250 cars during rush hourExplanation / Answer
Solution:-
2)
The probability that the hand is a royal flush is 0.00000154.
Total combination of royal flush = 4
Total number of combinations of different hands = 52C5 = 2,598,960
The probability that the hand is a royal flush is = 4/2598960 = 0.00000154.
3)
Probability of getting a full house = 0.001441
This hand has the pattern AAABB where A and B are from distinct kinds.
The number of such hands = 13C1 × 4C3 × 12C1 × 4C2. = 3774
Total number of combinations of different hands = 52C5 = 2,598,960
Probability of getting a full house = 3774/2,598,960 = 0.001441.
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