Answer to Question #143531 in Statistics and Probability for sara

Question

One card is randomly selected from a deck of cards. Find the odds against drawing a

red

seven

.

Answer 1

Answer 1)

Odds against drawing a red card = $\frac {Probability\ of\ drawing\ non-red\ card} {Probability\ of\ drawing\ red\ card}$

There are total 26 red cards & 26 non-red cards in a pack of 52 cards.

Probability of drawing a non-red card = $\frac {26C1}{52C1} = \frac {26}{52}=0.5$

Probability of drawing a red card = $\frac {26C1}{52C1} = \frac {26}{52}=0.5$

Hence the odds against drawing a red card = $\frac {0.5}{0.5}=1:1$

Answer 2)

Odds against drawing a seven = $\frac {probability\ of\ not\ drawing\ seven }{probability\ of\ drawing\ seven }$

There are total 4 Seven cards in a pack

Probability of not drawing a seven = $\frac {48C1}{52C1}=\frac {48}{52}$

Probability of drawing a seven = $\frac {4C1}{52C1}=\frac {4}{52}$

Hence the odds against drawing a seven = $\frac {\frac {48}{52}}{\frac {4}{52}}=\frac {48*52}{4*52}=\frac {48}{4}=12:1$