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

Find the probability of getting at most two heads.

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Solution

The total number of trials is 200.

Let A be the event of getting at most two heads.

The number of times A happens is.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have.

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Question 4
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
$\begin{matrix} Out come & 3 heads & 2 heads & 1 head & No head Frequency & 23 & 72 & 77 & 28 \end{matrix}$
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

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

$\begin{matrix} Outcome & 3 heads & 2 heads & 1 heads & 0 heads Frequency & 22 & 76 & 83 & 19 \end{matrix}$

What is the probability of getting

(i) not more than one head?
(ii) at least two heads?
(iii) exactly two heads? [3MARKS]

Q. Two coins were tossed simultaneously 80 times and the outcomes were recorded as under:

Outcome	Two heads	One head	No head
Frequency	24	36	20

If two coins are tossed at random, find the probability of getting
(i) two heads
(ii) one head
(iii) no head

Q. Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:

Outcome:	Two heads (HH)	One head (HT or TH)	No head (TT)
Frequency:	105	275	120

If same pair of coins is tossed at random, find the probability of getting (i) Two heads (ii) One head (iii) No head.

Q. Three coins are tossed simultaneously

200

times with the following frequencies of different outcomes:

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

If the three coins are simultaneously tossed again, compute the probability of

2

heads coming up.

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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 Find the probability of getting at most two heads.

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

Find the probability of getting at most two heads.