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Question

Three coins are tossed together. Find the probability of getting:
(i) exactly two heads
(ii) at least two heads
(iii) at least one head and one tail
(iv) no tails


Solution

When 3 coins are tossed together, the outcomes are as follows:S=h,h,h, h,h,t, h,t,h, h,t,t, t,h,h, t,h,t, t,t,h, t,t,tTherefore, the total number of outcomes is 8.(i)Let A be the event of getting triplets having exactly 2 heads.Triplets having exactly 2 heads: h,h,t, h,t,h, t,h,hTherefore, the total number of favourable outcomes is 3.PA=Number of favourable outcomesTotal number of outcomes=38(ii)Let A be the event of getting triplets having at least 2 heads.Triplets having at least 2 heads: h,h,t, h,t,h, t,h,h, h,h,hTherefore, the total number of favourable outcomes is 4.PA=Number of favourable outcomesTotal number of outcomes=48=12(iii)Let A be the event of getting triplets having at least one head and one tail.Triplets having at least one head and one tail: h,h,t, h,t,h, t,h,h, h,h,t, t,t,h, t,h,tTherefore, the total number of favourable outcomes is 6.PA=Number of favourable outcomesTotal number of outcomes=68=34(iv)Let A be the event of getting triplets having no tail.Triplets having no tail: h,h,hTherefore, the total number of favourable outcomes is 1.PA=Number of favourable outcomesTotal number of outcomes=18

Mathematics
RD Sharma (2019, 2020)
All

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