Question

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes- no head-14 one head-38 two heads-36 three heads-12 if the three coins are simultaneously tossed again,compute the probability of: 1. 2 heads coming up. 2. 3 heads coming up. 3. at least one head coming up. 4.getting more heads than tails. 5. getting more tails than heads.

Answer 1

Solution :-
Total number of outcomes = 100

Answer 1) : 2 heads coming up
Probability = 36/100
= 9/25
 
Answer 2) : 3 heads coming up 
Probability = 12/100
= 3/25

Answer 3) : At least 1 head coming up
Probability = (36/100 + 38/100 + 12/100)
= 86/100
= 43/50

Answer 4) : Getting more heads than tails
Number of times 2 heads (2 heads and 1 tail) appears = 36 
Number of times 3 heads (3 heads and 0 tail) appears = 12
Number of favorable outcomes = 36 + 12 = 48
Probability (Getting more heads than tails)
= Number of favorable outcomes/Total number of possible outcomes
= 48/100
= 12/25

Answer 5) : Getting more tails than heads
Number of times 2 tails (2 tails and 1 head) appears = 38
Number of times 3 tails (3 tails and 0 head) appears = 14
Number of favorable outcomes = 38 + 14 = 52
Probability (Getting more tails than heads) = 52/100
= 13/25

Answer 2

Solution :-

Total number of outcomes = 100

Answer 1) : 2 heads coming up

Probability = 36/100

= 9/25

 

Answer 2) : 3 heads coming up  

Probability = 12/100

= 3/25

Answer 3) : At least 1 head coming up

Probability = (36/100 + 38/100 + 12/100)

= 86/100

= 43/50

Answer 4) : Getting more heads than tails

Number of times 2 heads (2 heads and 1 tail) appears = 36  

Number of times 3 heads (3 heads and 0 tail) appears = 12

Number of favorable outcomes = 36 + 12 = 48

Probability (Getting more heads than tails)

= Number of favorable outcomes/Total number of possible outcomes

= 48/100

= 12/25

Answer 5) : Getting more tails than heads

Number of times 2 tails (2 tails and 1 head) appears = 38

Number of times 3 tails (3 tails and 0 head) appears = 14

Number of favorable outcomes = 38 + 14 = 52

Probability (Getting more tails than heads) = 52/100

= 13/25