6. In the Numbers Game, a state lottery, four numbers are drawn with replacement
ID: 2922384 • Letter: 6
Question
6. In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusive. Find the probability that two specified, consecutive digits in exact order are matched to the winning ticket. 7. Four cards are randomly drawn from a deck of 52 cards. You win $5 if the cards have at least one king. What is the probability that you will win the game? 8. A group of 20 people is selected at random. What is the probability that at least two of them have the same birthday?Explanation / Answer
6. The two specified consecutive digits can take three places in the winning number (first and second, second and third or third and fourth).
In each case, probability that the two digits match the numbers = 1/10 * 1/10 = 1/100.
=> Probability = 1/100 * 4 = 1/25 = 0.04.
7. The probability that a card is a king = 4/52 = 1/13
=> Probability that the card is not a king = 1 - 1/13 = 12/13
The probability that none of the cards are kings = (12/13)4
=> Probability of drawing atleast one king = 1 - 0.7620 = 0.2380.
8. The number of ways of assigning different birthdays to 20 people = 365P20
Probability of 20 people having different birthdays = 365P20 / (365)20
=> Probability that atleast two of them have the same birthday = / 17613971492896263399658990294901282502174377441406
25
= 0.5886.
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