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Question

Two coins are tossed simultaneously 500 times and
we get Two heads: 105 times
One head: 275 times
No head: 120 times
Find the probability of occurrence of each of these events

Solution
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$$\textbf{Step 1: Find probability by taking ratio of favorable outcomes to the total outcomes}$$
$$\text{Let E}_{1} = \text{event of getting two heads}$$
$$\text{E}_{2} = \text{event of getting one head}$$
$$\text{E}_{3} = \text{event of getting no head}$$

$$P\text{(Two heads)}=P(E_1 ) $$

$$\Rightarrow P\text{(Two heads)}= \dfrac{105}{500} $$$$\quad \quad \quad \left[\because\boldsymbol{P(E)=\dfrac{\textbf{Favorable outcomes}}{\textbf{Total outcomes}}}\right]$$

$$\Rightarrow P\text{(Two heads)}= 0.21$$

$$P\text{(Two heads)}=P(E_2 ) $$
$$\Rightarrow P\text{(One heads)}= \dfrac{275}{500} $$$$\quad \quad \quad \left[\because\boldsymbol{P(E)=\dfrac{\textbf{Favorable outcomes}}{\textbf{Total outcomes}}}\right]$$

$$\Rightarrow P\text{(Two heads)}= 0.55$$

$$P\text{(Two heads)}=P(E_3) $$
$$\Rightarrow P\text{(No heads)}= \dfrac{120}{500} $$$$\quad \quad \quad \left[\because\boldsymbol{P(E)=\dfrac{\textbf{Favorable outcomes}}{\textbf{Total outcomes}}}\right]$$

$$\Rightarrow P\text{(No heads)}= 0.24$$

$$\textbf{Hence, probabilities for 2 heads, 1 head, and no heads are 0.21, 0.33 and 0.24 respectively}$$

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Similar Questions
Q1

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes :

Two heads : 95 times

One tail : 290 times

No head : 115 times

Find the probability of occurrence of each these events.[NCERT]

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Q2
Two coins are tossed 250 times and the outcomes are:
(i) No heads = 70
(ii) One head = 85
(iii) Two heads = 95
Find the probability of the occurrence of each of these events.
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Q3
two coins are tossed 250 times and the out comes are
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Q4
Two coins are tossed 250 times and the outcomes are:
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[Experimental Probability]
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Q5
Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:
Outcome: Two heads
(HH)
One head
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No head
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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.
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