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# Three coins are tossed once. Find the probability of getting

(i) 3 Heads (ii) 2 Heads (iii)Atleast 2 Heads

(iv) Atmost 2 Heads (v) No Head (vi) 3 Tails

(vii) Exactly 2 Tails (viii) No Tail (ix) Atmost two tails

**Solution:**

When three coins are tossed once, the sample space is given by

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

Hence, n (S) = 8

It is known that the probability of an event A is given by

P (A) = Number of outcomes favourable to A/Total number of possible outcomes

= n (A)/n (S)

**(i)** Let B be the event of the occurrence of 3 heads.

Accordingly, B = {HHH}

= n (B)/n (S)

= 1/8

**(ii)** Let C be the event of the occurrence of 2 heads.

Accordingly, C ={HHT , HTH ,THH}

P (C) = n (C)/n(S)

= 3/8

**(iii)** Let D be the event of the occurrence of at least 2 heads.

Accordingly, D = {HHH, HHT, HTH, THH}

P (D) = n (D)/n(S)

= 4/8

= 1/2

**(iv)** Let E be the event of the occurrence of atmost 2 heads.

Accordingly, E = {HHT, HTH, THH, HTT, THT, TTH, TTT}

P (E) = n (E)/n(S)

= 7/8

**(v)** Let F be the event of the occurrence of no

Accordingly, F = {TTT}

P (F) = n (F)/n(S)

= 1/8

**(vi)** Let G be the event of the occurrence of 3 tails.

Accordingly, G = {TTT}

P (G) = n (G)/n(S)

= 1/8

**(vii)** Let H be the event of the occurrence of exactly 2 tails.

Accordingly, H = {HTT, THT, TTH}

P (H) = n (H)/n(S)

= 3/8

**(viii)** Let I be the event of the occurrence of no tail.

Accordingly, I = {HHH}

P (I) = n (I)/n(S)

= 1/8

**(ix)** Let J be the event of the occurrence of at most 2 tails.

Accordingly, J = {HHH, HHT, HTH, THH, HTT, THT, TTH}

P (J) = n (J)/n(S)

= 7/8

NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 8

## Three coins are tossed once. Find the probability of getting

(i) 3 Heads (ii) 2 Heads (iii)Atleast 2 Heads

(iv) Atmost 2 Heads (v) No Head (vi) 3 Tails

(vii) Exactly 2 Tails (viii) No Tail (ix) Atmost two tails

**Summary:**

Three coins are tossed once. Then the probabilities of the given events are: (i) 1/8 (ii) 3/8 (iii) 1/2 (iv) 7/8 (v) 1/8 (vi) 1/8 (vii) 3/8 (viii) 1/8 (ix) 7/8

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