The positions on a lacrosse team are called defenders (D), midfielders (M), and attackers (A). One player is chosen at random to
lead the team in
exercises before each game. The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two
games. The list of all possible outcomes is shown, where each outcome has equal probability of occurring.
AAA AMA ADA
MAA
MDA DAA DMA DDA
AAM AMM ADM MAM MMM MDM
DMM DDM
AAD AMD ADD MAD MMD MDD DAD DMD DDD
MMA
DAM
What is the probability that a defender is chosen at least once, given that a midfielder is chosen at the first game?
exercises before each game. The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two
games. The list of all possible outcomes is shown, where each outcome has equal probability of occurring.
AAA AMA ADA
MAA
MDA DAA DMA DDA
AAM AMM ADM MAM MMM MDM
DMM DDM
AAD AMD ADD MAD MMD MDD DAD DMD DDD
MMA
DAM
What is the probability that a defender is chosen at least once, given that a midfielder is chosen at the first game?
1 answer:
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Answers:
- Domain is (-4, 3]
- Range is (-5, 5]
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Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that . It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is . This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.