wo urns contain white balls and yellow balls. The first urn contains 3 white balls and 6 yellow balls and the second urn contain

Question

3 years ago

11

s 7 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?

2 answers:

vlada-n [284] · Answer 1 · 2022-03-12T09:58:29+03:00

Answer:

Answer is

$\frac{7}{30}$

Step-by-step explanation:

Given that there are two urns. First urn contains 3 white balls and 6 yellow balls and the second urn contains 7 white balls and 3 yellow balls.

A ball is drawn from each urn.

Probability for ball from urn I is white = no of white balls/total balls in I urn

$= \frac{3}{9} =\frac{1}{3}$

Probability for ball from urn II is white = no of white balls/total balls in I urn

$=\frac{7}{10}$

Since drawing one ball from each urn is independent of the other we find

Prob that both balls are white=

Prob that ball from I urn is white *Prob that ball from II urn is white

= $= \frac{7}{10} *\frac{1}{3}\\=\frac{7}{30}$

Tanya [424] · Answer 2 · 2022-03-12T11:54:43+03:00

The probability that both balls are white is 7/30

<h3>Further explanation</h3>

The probability of an event is defined as the possibility of an event occurring against sample space.

Let us tackle the problem.

If the first urn contains 3 white balls and 6 yellow balls , then the probability of picking up a white ball from the first urn is:

$P(W_1) = \frac{3}{3 + 6}$

$P(W_1) = \frac{3}{9}$

$\large {\boxed {P(W_1) = \frac{1}{3} } }$

If the second urn contains 7 white balls and 3 yellow balls , then the probability of picking up a white ball from the second urn is:

$P(W_2) = \frac{7}{3 + 7}$

$\large {\boxed {P(W_2) = \frac{7}{10} } }$

From the above results , the probability that both balls are white can be calculated using following formula:

$P( W_1 \bigcap W_2 ) = P(W_1) \times P(W_2)$

$P( W_1 \bigcap W_2 ) = \frac{1}{3} \times \frac{7}{10}$

$\large {\boxed {P( W_1 \bigcap W_2 ) = \frac{7}{30} } }$

<h2>Conclusion:</h2>

The probability that both balls are white is 7/30

<h3>Learn more</h3>

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Urn , White , Yellow , Ball , Random