Question

Three coins are tossed together. Find the probability of getting:
(a)exactly two heads
(b)at most two heads
(c)at least one head and one tail.
(d)no tails

Answer 1

SOLUTION :  

GIVEN: Three coins are tossed simultaneously.

When three coins are tossed then the possible outcome will be:  

TTT, THT, TTH, THH. HTT, HHT, HTH, HHH.

Total number of  outcomes =  8.

(i) Let E1 = Event of getting exactly two heads  

Then the outcome variable to E1 is THH, HHT ,HTH.

Number of outcomes favourable to E1 = 3

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = ⅜  

Hence, probability of getting exactly two head ,P(E1)  = ⅜ .  

(ii) Let E2 = Event of getting  at least two head  

Then the outcome variable to E2 is HHT, HTH, HHH ,THH

Number of outcomes favourable to E2 = 4

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 4/8 = ½  

Hence, probability of getting at least two head ,P(E2) = ½ .

(iiii) Let E3 = Event of getting  At least one head and one tail

Then the outcome variable to E3 is THT, TTH, THH, HTT, HHT, HTH,

Number of outcomes favourable to E3 = 6

Probability (E3) = Number of favourable outcomes / Total number of outcomes

P(E3) = 6/8 = 3/4

Hence, probability of getting At least one head and one tail ,P(E3)  = ¾ .

(iv) Let E4 = Event of getting  no tails  

Then the outcome variable to E4 is HHH

Number of outcomes favourable to E4 = 1

Probability (E4) = Number of favourable outcomes / Total number of outcomes

P(E4) = 1/8

Hence, probability of getting no tails ,P(E4) = ⅛  

HOPE THIS ANSWER WILL HELP  YOU…

Answer 2

Solution:

Total Possible outcomes when three coins tossed together
TTT
TTH
THT
THH
HTT
HTH
HHT
HHH

total outcomes = 8

1) Favourable outcome for getting exactly two heads:HHT,HTH,THH = 3

Probability of getting exactly two heads = 3/8


(b)at most two heads

Favourable conditions =TTT,TTH,THT,THH,HTT
HTH,HHT = 7

Probability of getting at most two heads = 7/8

C)at least one head and one tail:

Favourable conditions:TTH,THT,THH,HTT
HTH,HHT = 6

Probability of getting at least one head and one tail = 6/8 = 3/4

d)no tails:
Favourable conditions:HHH = 1
Probability of getting no tails = 1/8