Pls help....?

Question

A fair coin is flipped 10 times. Find the probability that 3 heads occur in the first 5 flips and in the last 5 flips. (Full solutions will be appreciated thanks.)

Answer 1

最佳解答

event (3 H in 1st 5 flips)

= {(H,H,H,T,T),(H,H,T,H,T),(H,H,T,T,H),(H,T,H,H,T),(H,T,H,T,H),(H,T,T,H,H), (T,H,H,H,T),(T,H,H,T,H),(T,H,T,H,H),(T,T,H,H,H)}

∴ no. of events (3 H in 1st 5 flips) = 10

no. of events (3 H in 1st 5 flips & last 5 flips) = 10×10 = 100

no. of events in sample space (a coin flipped 10 times) = 2^10

∴ probability (3 H in 1st 5 flips & last 5 flips) = 100/(2^10) = 25/256 (= 0.09765625)

[ Can answer as : probability = 0.098 (to 2 sig.fig.) ]

~~~~~~~~~~~~~~~~~~~~~~~~ COMPLETED ~~~~~~~~~~~~~~~~~~~~~~~~~~

Tips for counting :

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i) For the 1st 2 flips, events can be : HH,HT,TH,TT

ii) Fix the 1st 2 flips, then list the events of the coming 3 flips

(*remember -- 3 H in max. ) :

HH --> can follow by HTT, THT, TTH

HT --> can follow by HHT, HTH, THH

TH --> can follow by HHT, HTH, THH

TT --> can only follow by HHH