Question

Q and r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)

Answer 1

Answer:

(b) $\frac{7}{30}$

Step-by-step explanation:

When two p and q events are independent then, by definition:

P (p and q) = P (p) * P (q)

Then, if q and r are independent events then:

P(q and r) = P(q)*P(r) = 1/4*1/5

P(q and r) = 1/20

P(q and r) = 0.05

In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.

In the first ballot box there are 9 balls, 3 white and 6 yellow.

Then the probability of obtaining a white ball from the first ballot box is:

$P (W_{u_1}) = \frac{3}{9} = \frac{1}{3}$

In the second ballot box there are 10 balls, 7 white and 3 yellow.

Then the probability of obtaining a white ball from the second ballot box is:

$P (W_{u_2}) = \frac{7}{10}$

We want to know the probability of obtaining a white ball in both urns. This is: P($W_{u_1}$ and $W_{u_2}$)  

As the events are independent:

P($W_{u_1}$ and $W_{u_2}$)  = P ($W_{u_1}$) * P ($W_{u_2}$)

P($W_{u_1}$ and $W_{u_2}$)  = $\frac{1}{3}* \frac{7}{10}$

P($W_{u_1}$ and $W_{u_2}$)  = $\frac{7}{30}$

Finally the correct option is (b) $\frac{7}{30}$