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Home » Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3 ‘.
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3 ‘.
CBSE | Maths | NCERT | Probability
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3 ‘.

Let E be the event that ‘the coin shows a tail’ and F be the event that ‘at least one die shows a 3 ‘.

Rightarrow mathrm{E}={1 mathrm{~T}, 2 mathrm{~T}, 4 mathrm{~T}, 5 mathrm{~T}} and mathrm{F}={(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(6,3)}

Rightarrow E cap F=varphi Rightarrow P(E cap F)=0 ldots ldots ldots (i)

Now, we know that by definition of conditional probability, P(E mid F)=frac{P(E cap F)}{P(F)}

Rightarrow mathrm{P}(mathrm{E} mid mathrm{F})=frac{0}{mathrm{P}(mathrm{F})}=0

Rightarrow mathrm{P}(mathrm{E} mid mathrm{F})=0

i

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