These Ten-Year-Series (TYS) worked solutions with video explanations for 1995 A Level H2 Mathematics Paper 2 Question Q6 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
1995 A Level H2 Math Paper 2 Question 6
A bag contains $3$ red balls and $3$ green balls. Balls are drawn from the bag at random, one by one and without replacement.
(a)
Show that the probability that the first $3$ balls drawn are red is $\frac{1}{20}$.
[1]
(a) Show that the probability that the first $3$ balls drawn are red is $\frac{1}{20}$.
[1]
(b)
Find the probability that the first $3$ balls drawn consist of $2$ red balls and $1$ green ball (in an order). Hence, or otherwise show that the probability that the third red appear on the fourth draw is $\frac{3}{20}$.
[2]
(b) Find the probability that the first $3$ balls drawn consist of $2$ red balls and $1$ green ball (in an order). Hence, or otherwise show that the probability that the third red appear on the fourth draw is $\frac{3}{20}$.
[2]
(c)
Find the probability that the third red ball appears on the fifth draw.
[2]
(c) Find the probability that the third red ball appears on the fifth draw.
[2]
(d)
The random variable $X$ is the number of draws required up to and including the one on which the third red ball appears. Tabulate the probability distribution of $X$ and find $\text{E}\left( X \right)$.
[4]
(d) The random variable $X$ is the number of draws required up to and including the one on which the third red ball appears. Tabulate the probability distribution of $X$ and find $\text{E}\left( X \right)$.
[4]
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