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Elena-2011 [213]
3 years ago
10

Two cards are drawn from a well shuffled standard deck of cards of cards. Match each scenario to its probability

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Step-by-step explanation:

"The probability of drawing a red ace followed by another ace of any color without replacement."

There are 4 aces total, 2 of which are red.  After the first red ace is drawn, there will be 3 aces left.  So the probability is:

P = (2/52) (3/51)

P = 1/442

"The probability of drawing a king followed by a queen with replacement."

There are 4 kings and 4 queens.  So the probability is:

P = (4/52) (4/52)

P = 1/169

"The probability of drawing a 3 or a 5 followed by a 4 or a 6 with replacement."

There are 8 cards that are either 3 or 5, and 8 cards that are either 4 or 6.  So the probability is:

P = (8/52) (8/52)

P = 4/169

"The probability of drawing a spade followed by a jack of any color with replacement."

There are 13 spades, and 4 jacks.  So the probability is:

P = (13/52) (4/52)

P = 1/52

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Here we go !!

Since it's a regular pentagon, all it's sides are equal so let's solve for x

\hookrightarrow \: 3(x - 1)  = 5x - 6

\hookrightarrow \: 3x - 3 = 5x - 6

\hookrightarrow \:  3x - 5x =  - 6 + 3

\hookrightarrow \:  - 2x =  - 3

\hookrightarrow \: x =  \dfrac{ - 3}{ - 2}

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now let's find the measure of each side, i.e

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\hookrightarrow \: (5 \times  \dfrac{3}{2})  - 6

\hookrightarrow \:  \dfrac{15}{2}   - 6

\hookrightarrow \: 7.5 - 6

\mathrm{\hookrightarrow \: 1.5 \: units}

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\hookrightarrow \: 1.5 \times 5

\boxed{ \boxed{ \:  \:  \:  \:  \:  \:  \:  \: 7.5 \:  \:  units \:  \:  \:  \:  \:    \:  \:  }}

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