<p>A bag contains $3$ red balls and $3$ green balls. Balls are drawn from the bag at random, one by one and without replacement.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Show that the probability that the first $3$ balls drawn are red is $\frac{1}{20}$.</span></div><p style="text-align: right;">[1]</p></li><li><div class="list-item-content"><span class="list-item-text">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 $\frac{3}{20}$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the probability that the third red ball appears on the fifth draw.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">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 $\mathrm{E}\left( X \right)$.</span></div><p style="text-align: right;">[4]</p></li></ol>

A bag contains $3$ red balls and $3$ green balls. Balls are drawn from the bag at random, one by one and without replacement.

Show that the probability that the first $3$ balls drawn are red is $\frac{1}{20}$.

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 $\frac{3}{20}$.

Find the probability that the third red ball appears on the fifth draw.

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 $\mathrm{E}\left( X \right)$.

N1995 P2 Q6

N1995 P2 Q6

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