Math  /  Data & Statistics

QuestionThe given jar contains yellow ( YY ), blue (B), and red (R) balls. Anne randomly chooses a single ball from the can shown here. Find the odds against the event. red or yellow ( R or Y )
State the odds against red or yellow in lowest terms. The odds against red or yellow are \square to \square (Type whole numbers.)

Studdy Solution

STEP 1

1. The jar contains 7 red balls, 1 yellow ball, and 4 blue balls.
2. The total number of balls is the sum of red, yellow, and blue balls.
3. The odds against an event are calculated as the ratio of the probability of the event not occurring to the probability of the event occurring.

STEP 2

1. Calculate the total number of balls.
2. Calculate the probability of drawing a red or yellow ball.
3. Calculate the probability of not drawing a red or yellow ball.
4. Calculate the odds against drawing a red or yellow ball.

STEP 3

Calculate the total number of balls:
7(red)+1(yellow)+4(blue)=12(total balls) 7 \, (\text{red}) + 1 \, (\text{yellow}) + 4 \, (\text{blue}) = 12 \, (\text{total balls})

STEP 4

Calculate the probability of drawing a red or yellow ball:
P(RorY)=7(red)+1(yellow)12(total balls)=812=23 P(R \, \text{or} \, Y) = \frac{7 \, (\text{red}) + 1 \, (\text{yellow})}{12 \, (\text{total balls})} = \frac{8}{12} = \frac{2}{3}

STEP 5

Calculate the probability of not drawing a red or yellow ball (i.e., drawing a blue ball):
P(not(RorY))=4(blue)12(total balls)=13 P(\text{not} \, (R \, \text{or} \, Y)) = \frac{4 \, (\text{blue})}{12 \, (\text{total balls})} = \frac{1}{3}

STEP 6

Calculate the odds against drawing a red or yellow ball:
The odds against an event is the ratio of the probability of the event not occurring to the probability of the event occurring:
Odds against(RorY)=P(not(RorY))P(RorY)=1323=12 \text{Odds against} \, (R \, \text{or} \, Y) = \frac{P(\text{not} \, (R \, \text{or} \, Y))}{P(R \, \text{or} \, Y)} = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2}
Thus, the odds against drawing a red or yellow ball are 11 to 22.
The odds against red or yellow are:
1to2 \boxed{1} \, \text{to} \, \boxed{2}

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