Question

Two coins are tossed simultaneously. Find the probabillity of getting

(i) no head (ii) exactly one tail (iii) atleast one head (iv) at most one tails​

Answer 1

Answer:

i) When two coins are tossed the outcomes will be: {HH, HT, TH, TT}. So getting no head in any coin then both of the coin must show the result TT. Now this result occurs only 1 time in the sample set. So the probability of getting no head is ¼.

ii) Let E3 = event of getting 1 tail. Then,

E3 = {TH, HT} and, therefore, n(E3) = 2.

Therefore, P(getting 1 tail) = P(E3) = n(E3)/n(S) = 2/4 = 1/2

iii) Let E6 = event of getting at least 1 head. Then,

E6 = {HT, TH, HH} and, therefore, n(E6) = 3.

Therefore, P(getting at least 1 head) = P(E6) = n(E6)/n(S) = ¾.

iv) Let E7 = event of getting at least 1 tail. Then,

E7 = {TH, HT, TT} and, therefore, n(E7) = 3.

Therefore, P(getting at least 1 tail) = P(E2) = n(E2)/n(S) = ¾.

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