Question

( 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.

# 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)

Solution