A BINGO card consists of a square containing 25 smaller squa

              A BINGO card consists of a square containing 25 smaller squares, as shown in the figure. Five numbers from 1 to 15 are placed under the letter B, five numbers from 16 to 30 are placed under the letter I, four numbers from 31 to 45 along with the “free space” are placed under the letter N, five numbers from 46 to 60 are placed under the letter G, and five numbers from 61 to 75 are placed under the letter O. When a regular Bingo game is played, the numbers from 1 to 75 are randomly called until someone’s card has five numbers in a horizontal, vertical, or diagonal row. Suppose you are playing Bingo with the card in the figure. Answer the following questions:

a. What is the probability that the first number called is on your card?

b. What is the probability that G-59 is the first number called?

c. What is the probability that the first number called is in your N column?

d. Suppose the first number called is not on your card. What is the probability that the second

     number called is on your card?

Solution

a)

There are 25 on your card, out of the 75 possible.

Thus,

P = 25/75 = 1/3 or 0.33333333 [answer]

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b)

G-59 is just 1 out of 75 possibilities.

Hence,

P(G-69) = 1/75 or 0.013333333 [answer]

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c)

There are 5 numbers on your N column, out of the 75 drawn.

Thus,

P(N) = 5/75 = 1/15 or 0.066666667 [answer]

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d)

There are just 74 balls in the draw, and you still have 25 numbers.

Thus,

P = 25/74 or 0.337837838 [answer]