The names of the months of the year
were written on separate papers and
placed in a hat. Two papers are ran-
domly drawn one at a time, replacing
the first before the second draw. What
is the probability of drawing. ?
(a) April and then June
(b) a month ending in r and then a
month ending in y
(c) May and then not drawing May


Write the probability as a reduced fraction

Step-by-step explanation:

There are 12 months of the year, so there are 12 possible choices for each draw. Since the first paper is replaced before the second draw, each draw can be considered as independent and with replacement.

(a) To draw April and then June, we need to draw April on the first draw (with probability 1/12), and then June on the second draw (with probability 1/12). The probability of both events happening is the product of their probabilities:

P(April and then June) = (1/12) x (1/12) = 1/144

(b) To draw a month ending in r and then a month ending in y, we can choose from the following months: April, June, July, September, and November. There are 5 months that end in r, so the probability of drawing one of them on the first draw is 5/12. After replacing the first paper, there are still 12 months left in the hat, but now we want to draw a month ending in y. There are 4 months that end in y, so the probability of drawing one of them on the second draw is 4/12. Again, the probability of both events happening is the product of their probabilities:

P(month ending in r and then month ending in y) = (5/12) x (4/12) = 5/36

(c) To draw May on the first draw and not draw May on the second draw, the probability of drawing May on the first draw is 1/12, and the probability of not drawing May on the second draw is 11/12 (since there are 11 months left in the hat after May is drawn on the first draw). Again, the probability of both events happening is the product of their probabilities:

P(May and then not drawing May) = (1/12) x (11/12) = 11/144

Therefore, the probabilities are:

(a) 1/144

(b) 5/36

(c) 11/144

Step-by-step explanation:

There are 12 months of the year, so there are 12 possible choices for each draw. Since the first paper is replaced before the second draw, each draw can be considered as independent and with replacement.

(a) To draw April and then June, we need to draw April on the first draw (with probability 1/12), and then June on the second draw (with probability 1/12). The probability of both events happening is the product of their probabilities:

P(April and then June) = (1/12) x (1/12) = 1/144

(b) To draw a month ending in r and then a month ending in y, we can choose from the following months: April, June, July, September, and November. There are 5 months that end in r, so the probability of drawing one of them on the first draw is 5/12. After replacing the first paper, there are still 12 months left in the hat, but now we want to draw a month ending in y. There are 4 months that end in y, so the probability of drawing one of them on the second draw is 4/12. Again, the probability of both events happening is the product of their probabilities:

P(month ending in r and then month ending in y) = (5/12) x (4/12) = 5/36

(c) To draw May on the first draw and not draw May on the second draw, the probability of drawing May on the first draw is 1/12, and the probability of not drawing May on the second draw is 11/12 (since there are 11 months left in the hat after May is drawn on the first draw). Again, the probability of both events happening is the product of their probabilities:

P(May and then not drawing May) = (1/12) x (11/12) = 11/144

Therefore, the probabilities are:

(a) 1/144

(b) 5/36

(c) 11/144

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Bus 18, with an IQR of 7

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Bus 18, with a range of 7