Question

Mark has 3 marbles in his pocket. 2 marbles are yellow and one is blue. if he randomly selects two marbles, what is the probability that they are the same colour?
2/9. 4/9. 2/3. 1/3. ​

Answer 1

${\pmb{\sf{\underline{\maltese \: \: Understanding \: the \: Question...}}}}$

★ This question says that a boy Mark has total 3 marbles in his pocket. Two marbles are yellow in colour and one is in blue colour. If he selects two marbles, what is the probability that they are the same colour?

${\pmb{\sf{\underline{\maltese \: \: Given \; that...}}}}$

• Total marbles = Three

• Marbles colour-Yellow and Blue

• Yellow marble = Two

• Blue marble = One

${\pmb{\sf{\underline{\maltese \: \: To \; find...}}}}$

• If he selects two marbles, what is the probability that they are the same colour?

${\pmb{\sf{\underline{\maltese \: \: Solution...}}}}$

• He selects two marbles, 2/3 is the probability that they are the same colour.

${\pmb{\sf{\underline{\maltese \: \: Explaination...}}}}$

He selects two marbles, 2/3 is the probability that they are the same colour. It is because he just have three marbles and two are of same colour and the formula to find probability says that

Probability of an event =

$\star\;\boxed{\sf{\pink{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}}$

Here, favourable number of outcomes are 2 and total number of outcomes are 3.

${\pmb{\sf{\underline{\maltese \: \: Additional \; knowledge...}}}}$

• A “random experiment” is one whose outcomes cannot be predicted exactly in advance.

• There are certain experiments whose outcomes have an equal chance of occuring.

• Outcomes of an experiment are “equally likely” if each has the same chance of occuring.

• Probability of an event: $\bigstar\;\boxed{\sf{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}$

• Chances and probability are related to real life.

• One or more outcomes of an experiment make an “event”.

Answer 2

Answer:

Total no of marbles=3

Total no of possible cases in selecting 2 marbles is the combination of 3 marbles taken 2 at a time.

n=total no of possible case =C(3,2)=3

For the favourable cases of 2 same(yellow) marbles,we find the combination of 2 same marbles out of 2 yellow marbles (there is only one blue marble).

m=no of favourable cases=C(2,2)=1

P(both are yellow marble)=m/n

=1/3 ans.