Question

If three coins are tossed three times find the probability of getting:-
a) at least one tail
b) exactly two head
c) at most two head​

Answer 1

$\huge\colorbox{pink}{Answer:-}$

When 3 coins are tossed, the possible outcomes are HHH, TTT, HTT, THT, TTH, THH, HTH, HHT.

The sample space is S = { HHH, TTT, HTT, THT, TTH, THH, HTH, HHT}

$\huge\colorbox{green}{Explanation:-}$

Number of elements in sample space, n(S) = 8

(i) Let E1 denotes the event of getting all tails.

E1 = {TTT}

n(E1) = 1

P(getting all tails) = n(E1)/ n(S)

= ⅛

Hence the required probability is ⅛.

(ii) Let E2 denotes the event of getting two heads.

E2 = {HHT, HTH, THH}

n(E2) = 3

P(getting two heads) = n(E2)/ n(S)

= 3/8

Hence the required probability is ⅜.

(iii) Let E3 denotes the event of getting atleast one head.

E3 = { HHH, HTT, THT, TTH, THH, HTH, HHT }

n(E3) = 7

P(getting atleast one head) = n(E3)/ n(S)

= 7/8

Hence the required probability is 7/8.

(iv) Let E4 denotes the event of getting one head.

E4 = { HTT, THT, TTH}

n(E4) = 3

P(getting one head) = n(E4)/ n(S)

= 3/8

Hence the required probability is 3/8.