Aussie Maths & Science Teachers: Save your time with SmarterEd
A coin is biased so that it is twice as likely to show a head than a tail.
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a. \(P(H) = \dfrac{2}{3}\)
b. \(P\text{(at least 1 head)}\ = \dfrac{8}{9}\)
a. \(P(H) = \dfrac{2}{3}\)
b. \(P(T) = 1-P(H)=1-\dfrac{2}{3}=\dfrac{1}{3}\)
| \(P\text{(at least 1 head)}\) | \(=1-P\text{(no heads)}\) | |
| \(=1-P(TT)\) | ||
| \(=1-\dfrac{1}{3} \times \dfrac{1}{3}=\dfrac{8}{9}\) |
The probability of winning a game is `7/10`.
Which expression represents the probability of winning two consecutive games?
`D`
`text{Since the two events are independent:}`
`P text{(W)}= 7/10`
`P text{(WW)}= 7/10 xx 7/10`
`=>D`
Each time she throws a dart, the probability that Mary hits the dartboard is `2/7`.
She throws two darts, one after the other.
What is the probability that she hits the dartboard with both darts?
`B`
`P text{(hits)} = 2/7`
`P text{(hits twice)}= 2/7 xx 2/7= 4/49`
`=> B`
In Mathsville, there are on average eight rainy days in October.
Which expression could be used to find a value for the probability that it will rain on two consecutive days in October in Mathsville?
`D`
`P text{(rains)} = 8/31\ \ \text{(independent event for each day)}`
`text{Since each day has same probability:}`
`P(R_1 R_2) = 8/31 xx 8/31`
`=> D`
The probability that Michael will score more than 100 points in a game of bowling is `31/40`.
Is the commentator correct? Give a reason for your answer. (1 mark)
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a. `text{Incorrect. Less than “or equal to 100” is correct.}`
b. `961/1600`
a. `text(The commentator is incorrect. )`
`text(The correct statement is)\ Ptext{(score} <=100 text{)} =9/40`
`text{(i.e. less than “or equal to 100” is the correct statement)}`
b. `P(text{score >100 in both})= 31/40 xx 31/40= 961/1600`