A game involves throwing a die and spinning a spinner.
The sum of the two numbers obtained is the score.
The table of scores below is partially completed.
What is the probability of getting a score of 7 or more?
- `1/6`
- `1/4`
- `5/18`
- `5/12`
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A game involves throwing a die and spinning a spinner.
The sum of the two numbers obtained is the score.
The table of scores below is partially completed.
What is the probability of getting a score of 7 or more?
A game involves rolling two six-sided dice, followed by rolling a third six-sided die. To win the game, the number rolled on the third die must lie between the two numbers rolled previously. For example, if the first two dice show 1 and 4, the game can only be won by rolling a 2 or 3 with the third die.
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i. `text(Construct a sample space of the number)`
COMMENT: Constructing the full sample space is a critical step here..
`text(of possible winning rolls:)`
`text{P(no chance)}` | `= text(number of pairs with no gap)/text(total possibilities)` |
`= 16/36` | |
`= 4/9` |
ii. `text(The sample space in the table shows:)`
`text(→ 8 combinations leave a gap for a single winning number,)`
`text(→ 6 combinations leave a gap for two winning numbers,)`
`vdots`
`:.\ text{P(winning)}` | `= 1/36 [8 xx 1/6 + 6 xx 2/6 + 4 xx 3/6 + 2 xx 4/6]` |
`= 1/36 (8/6 + 12/6 + 12/6 + 8/6)` | |
`= 1/36 (40/6)` | |
`= 5/27` |
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice.
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i. |
`:. P(0) = (11)/(36)`
ii. `P(≥ 16)= 4/36=1/9`
iii. `Ptext{(Sum} < 45) = 1 − Ptext{(Sum} ≥ 45)`
`Ptext{(Sum} ≥ 45)` | `=P(20,25)+P(25,20)+P(25,25)` |
`=(2/36 xx 1/36) + (2/36 xx 1/36)+(1/36 xx 1/36)` | |
`=2/1296 + 2/1296+ 1/1296` | |
`=5/1296` |
`:.Ptext{(Sum} < 45)` | `= 1 − 5/1296` |
`= 1291/1296` |
Two ordinary dice are rolled. The score is the sum of the numbers on the top faces.
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