A 'bingo' card has 5 columns and 5 rows. The 5 columns are labeled B,I,N,G,O. The squares in the 'B' column contain numbers from 1-15, chosen randomly. The square in the 'I','N','G', and 'O' columns contain numbers from 16-30, 31-45,46-60, and 61-75 respectively. All numbers are chosen randomly. The square in the center of the card (in the I column) is marked 'Free'.Each player has a bingo card. The Bingo master has a pot containing 75 markers that correspond to the 75 possible markings of the Bingo squares--i.e. B1-B15,I16-I30,…O61-O75. He chooses markers randomly one by one without replacement, and calls out the letter and number. A player gets 'Bingo' if he gets 5 numbers in a row, or 5 numbers in a column, or 5 on the diagonal (note the '0' is the center is automatically filled). A) What is the probability of a player getting 'Bingo' when the 4th number is chosen? B) What is the probability that there will be exactly 2 B's and 3 I's in the first 10 numbers? C) What is the probability that the first 5 markers will have exactly one of each letter B,I,N,G,O (order doesn't matter)? D) Suppose you arrive late at a Bingo game. The Bingo master has already called 3 markers. You see on the Bingo master's table that the three chosen markers are B12, N31, O62. What is the probability that the three markers were called in increasing order?
A 'bingo' card has 5 columns and 5 rows. The 5 columns are labeled B,I,N,G,O. The squares in the 'B' column contain numbers from 1-15, chosen randomly. The square in the 'I','N','G', and 'O' columns contain numbers from 16-30, 31-45,46-60, and 61-75 respectively. All numbers are chosen randomly. The square in the center of the card (in the I column) is marked 'Free'.Each player has a bingo card. The Bingo master has a pot containing 75 markers that correspond to the 75 possible markings of the Bingo squares--i.e. B1-B15,I16-I30,…O61-O75. He chooses markers randomly one by one without replacement, and calls out the letter and number. A player gets 'Bingo' if he gets 5 numbers in a row, or 5 numbers in a column, or 5 on the diagonal (note the '0' is the center is automatically filled).
A) What is the
B) What is the probability that there will be exactly 2 B's and 3 I's in the first 10 numbers?
C) What is the probability that the first 5 markers will have exactly one of each letter B,I,N,G,O (order doesn't matter)?
D) Suppose you arrive late at a Bingo game. The Bingo master has already called 3 markers. You see on the Bingo master's table that the three chosen markers are B12, N31, O62. What is the probability that the three markers were called in increasing order?
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