Question

A coin is tosses. If it shows head, we draw a ball from a bag consisting of $3$ red balls and $4$ black balls. If it shows a tail, we throw a dice. What is the sample space of this experiment? What are the favourable cases representing the events. (i) the throw of the coin resulted in a head. (ii) a red ball is drawn.

Answer 1

A Coin is tossed : Sample space $=[H,T]$

A bag contains $3$ red and $4$ black balls. If the coin shows head, we draw a ball from the bag.

$\Rightarrow$ Sample space $=3$ red $+$ $4$ black balls.

If it shows tail, a dice is thrown

$\therefore 6=[1,2,3,4,5]$

$1).$ A throw of coin resulted in head $=\frac{1}{2}$

Probability of getting a head $=\frac{1}{2}$

A ball can be drawn from the bag., $\frac{{}^3{C}_1\times 4C_1}{{}^7{C}_1}$

$=\frac{3\times 4}{7}$

$=\frac{12}{7}$

$2).$ A red ball is drawn when the coin shows head i.e, $\frac{{}^3{C}_1}{{}^7{C}_1}$

$=\frac{3}{7}.$

Hence, solved.