Can you help me with this algebra 2 question?

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1 Answer
Mar 31, 2018

#color(red)(a.))#, #7/12#

#color(red)(b.))#, #11/18#

Explanation:

.
#color(red)(a.))#

The probability of selecting a gold card is:

#36/72=1/2#

Between #1# and #72#, the numbers that are multiples of #12# are:

#12, 24, 36, 48, 60, and 72#

There are a total of #6# cards in the deck with multiples of #12# on them.

The probability of selecting one of these #6# is:

#6/72=1/12#

Therefore, the probability of selecting a gold card or a card with multiple of #12# on it would be the sum of the two probabilities:

#1/2+1/12=7/12#

#color(red)(b.))#

Similarly, the probability of selecting a silver card is:

#1/2#

Between #1# and #72#, the numbers that are multiples of #9# are:

#9, 18, 27, 36, 45, 54, 63, 72#

There are a total of #8# cards in the deck with multiples of #9# on them.

The probability of selecting one these #8# is:

#8/72=1/9#

Therefore, the probability of selecting a silver card or a card with multiple of #9# is the sum of the two probabilities:

#1/2+1/9=11/18#