Question

Three coins are tossed together. Find the probability of getting) Exactly one head (ii) At most two heads (iii)At least one head and one tail (iv) No tail​

Answer 1

Answer:

Hi mate

Step-by-step explanation:

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

Answer:

3/8, 7/8, 3/4, 1/7

Step-by-step explanation:

Cases=

HHH

HHT

HTH

THH

HTT

THT

TTH

TTT

i) exactly 1 head= 3/8

ii) almost 2 heads= zero heads + one head + two heads

=1/8+3/8+3/8=7/8

you can also do almost 2 heads= 1-3 heads =1-1/8=7/8

iii) atleast 1 head and 1 tail= 1-(no head+no tail)

=1-(1/8+1/8)=1-2/8=6/8=3/4

iv)no tail= 1 case (HHH)=1/7