JEE Mains · Maths · STD 11 - 14. probability
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
- A \(\frac{275}{6^{5}}\)
- B \(\frac{36}{5^{4}}\)
- C \(\frac{181}{5^{5}}\)
- D \(\frac{46}{6^{4}}\)
Answer & Solution
Correct Answer
(D) \(\frac{46}{6^{4}}\)
Step-by-step Solution
Detailed explanation
\(P ( H )= x , P ( T )=1- x\) \(P (4 H , 1 T )= P (5 H )\) \({ }^{5} C _{1}( x )^{4}(1- x )^{1}={ }^{5} C _{5} x ^{5}\) \(5(1- x )= x\) \(6 x =5=0 \quad x =\frac{5}{6}\) \(P (\) atmost \(2 H )\) \(= P ( OH , 5 T )+ P (1 H , 4 T )+ P (2 H , 3 T )\)…
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