Question

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

Answer 1

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`