Question

2 luo. Write down the binomial probability distribution of the number of successes in n independent trials when the chance of success in a single trial is P. In an experiment, 8 unbiased coins are tossed together. In how many out of 100 such experiments would one expect to obtain: (i) 3 'heads' and 5 'tails'; (ii) an equal number of 'heads' and 'tails'? Which of the two cases is more likely? (WAEC)

JEE/Engineering Exams

Maths

Solution

134

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( P=frac{1}{2} ) is trobability of 3 'heads & 5 'tails" [ ={ }^{b} c_{3}left(frac{1}{2}right)^{3}left(frac{1}{2}right)^{5}=frac{8}{2^{8}}=frac{7}{32} ] Number of experiments out of 100 which can show above prob [ left.=frac{7}{32} times 100=21 cdot 875 Rightarrow 2right) ] (ii) Probability of getfiy equal no. 8 'heads' & 'taics' = ( c_{4}left(frac{1}{2}right)^{4}left(frac{1}{2}right)^{4}=frac{8 c_{4}}{2^{8}}=frac{35}{128} ) Nuncher of such experincest out of 100 [ =frac{35}{128} times 100=27 cdot 34 text { in } 27 ] Second case is more likely to ocurr.