A) \[\frac{3}{4}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{3}\]
D) None of these
Correct Answer: A
Solution :
[a] Probability of getting a head in a single toss of a coin \[=1/2\left( =p \right)\] say Probability of getting 5 or 6 in a single throw of a die \[=1/3\left( =q \right)\] say Required probability \[=p+\left( 1-p \right)\left( 1-q \right)p+\left( 1-p \right)\left( 1-q \right)\left( 1-p \right)\left( 1-q \right)p+.....\]\[=p+\left( 1-p \right)\left( 1-q \right)p+{{\left( 1-p \right)}^{2}}{{\left( 1-q \right)}^{2}}p+......\]\[=\frac{p}{1-(1-p)(1-q)}=\frac{1/2}{1-1/2\times 2/3}=\frac{3}{4}\] Hence, option [b] is correct.
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