Question 19
Four coins are tossed simultaneously. What is the probability that two consecutive heads never occur together?
Solution
Probability of 2 consecutive heads being never together = 1 - Probability of 2 consecutive heads being together.
Cases where 2 heads are consecutive :
HHHH = 1 case.
THHH, HTHH, HHTH and HHHT = 4 cases.
HHTT, THHT and TTHH = 3 cases.
Total cases where 2 heads come consecutively = 8 cases.
Total number of possible cases with 4 coins = 2*2*2*2 = 16.
Probability of 2 consecutive heads = 8/16 = 1/2.
Now, Probability of 2 consecutive heads being never together = 1 - 1/2 = 1/2 i.e. Option D.
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