1.

Find the probability of almost two tails or almost two heads in a toss of three coins.

Answer»

When we toss three coins, the sample space is– 

S = {HHH, HHT, HTH, HTT, THH, TTH, TTT} 

⇒ n(S) = 8. 

Let ‘A’ and ‘B’ be the event of getting almost two tails and atmost two heads respectively. 

∴ A = {HHH, HHT, HTH, HTT. THH, THT, TTH} 

⇒ n(A) = 7 

and B = {HHT, HTH, HTT, THH, THT, TTH, TTT} 

⇒ n(B) = 7

 A ∩ B = {HHT, HTH, HTT, THH, THT, TTH) 

⇒ n(A ∩ B) = 6

∴ P(A) = \(\frac{n(A)}{n(S)}= \frac{7}{8}\), P(B) = \(\frac{n(B)}{n(S)}= \frac{7}{8}\)

P(A ∩ B) = \(\frac{n(A∩B)}{n(S)}=\frac{6}{8}\)

We know– 

P(A ∪ B) = P(A) + P(B): P(A ∪ B)

= \(\frac{7}{8}+\frac{7}{8}- \frac{6}{8}\)

= \(\frac{8}{8}\)

= 1.


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