JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q17

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MathematicsSingle correct+4 / -1Question 17 of 90

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :

\dfrac{275}{6^5}

\dfrac{36}{5^4}

\dfrac{181}{5^5}

\dfrac{46}{6^4}

Answer and worked solution

Official answer: D

Find p. $5p^4q=p^5$ , so $p=5q$ : $p=\frac56$ , $q=\frac16$ .

At most two heads. $q^5+5pq^4+10p^2q^3=\dfrac{1+25+250}{6^5}=\dfrac{276}{6^5}=\dfrac{46}{6^4}$ .

(D)

Topics:Binomial distribution

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JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 17