Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads - Mathematics

Sum

Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads

#### Solution

Sample space = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

n(S) = 8

Let A be the event of getting atmost 2 tails.

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

n(A) = 7

P(A) = ("n"("A"))/("n"("S")) = 7/8

Let B be the event of getting atleast 2 heads.

B = {HHH, HHT, HTH, THH}

n(B) = 4

P(B) = ("n"("B"))/("n"("S")) = 4/8

A ∩ B = {HHH, HHT, HTH, THH}

n(A ∩ B) = 4

P(A ∩ B) = ("n"("A" ∩ "B"))/("n"("S")) = 4/8

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

= 7/8 + 4/8 - 4/8

= 7/8

Probability of getting atmost two tails or atleast 2 heads = 7/8

Concept: Algebra of Events
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