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.

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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) = $52 / 100$
= $13 / 25$

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Outcome:	No head	One head	Two heads	Three heads
Frequency:	14	38	36	12

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Outcome	$3 h e a d s$	$2 h e a d s$	$1 h e a d$	No head
Frequency	$23$	$72$	$77$	$28$

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\begin{matrix} O u t c o m e & 3 h e a d s & 2 h e a d s & 1 h e a d & N o h e a d F r e q u e n c y & 23 & 72 & 77 & 28 \end{matrix}

Three coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:

Outcome	$3$ heads	$2$ heads	$1$ head	No head
Frequency	$23$	$72$	$77$	$28$

If the three coins are simultaneously tossed again, compute the probability of $2$ heads coming up.

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