Question

a coin is tossed 1000 times with the following frequencies:
Head:455 Tail:545
Compute the probability of each event.​

Answer 1

$\bigstar \bold{ \underline{ Concept}} \bigstar$

Here in this query , a coin is tossed 1000 times and Head comes up 455 times and Tail comes up 545 times. Here we have to calculate the probability for both head and tail. By applying the formula of probability we can get the value of both head and tail.

$\bigstar \bold{ \underline{ Solution}} \bigstar$

Let,

• the event of getting a head be E

• the event of getting a tail be F

Total no. of trials ➛ 455 + 545

ㅤㅤㅤㅤㅤㅤㅤㅤ➛ 1000

We know,

$\small\bigstar {\underline {\boxed { \rm {\green\:P(E)= \frac{Number \: of \: trials \: in \: which \: the \: event \: happened}{The \: Total \: number \: of \: trials} }}}} \bigstar$

$\small \rm \therefore {Probability \: of \: getting \: a \: head➛ \frac{Number \: of \: Heads}{Total \: number \: of \: Trials} }\:$

$\small \rm \implies \: P(E)\:➛ \frac{455}{1000} \\ \small \quad \quad \quad \quad \quad \rm ➛ \: \: \boxed{ .455}$

$\small \rm \therefore {Probability \: of \: getting \: a \: tail➛ \frac{Number \: of \: tails}{Total \: number \: of \: Trials} }\:$

$\small \rm \implies \: P(F)\:➛ \frac{545}{1000} \\ \small \quad \quad \quad \quad \quad \rm ➛ \: \: \boxed{ .545}$

$\bigstar \bold{ \underline{ Explore \: More}} \bigstar$

Let, us know more about Probability . By some defination . The definitions are given from the maths book of class 9 . Chapter ➡️ 15 , Chapter name ➡️ Probability.

• Trial:- ㅤA Trial is an action which results in one or several outcomes.

• Event:- ㅤAn event for an experiment is the collection of some outcomes of the experiment.

• Empirical Probability:- ㅤ Based on what we directly observe as the outcomes of our trial , we find the empirical or experimental probability.

$\\ \bigstar{ \underline{ \underline \pink{ \sf★@iTzShInNy☆}}} \bigstar$

Answer 2

Step-by-step explanation:

Given:  A coin is tossed 1000 times with the following frequencies:

Head: 455, Tail: 545

Total number of trials = 1000.

Let us denote the events of getting head and event of getting tail be E and F .

Number of trials in which the event E happens = 455

So, Probability ( E) = (Number of trials in which the event E happens) / (Total number of trials)

P(E) = 455/1000  

P(E) = 0.455

Probability of the event getting a tail, P(E) =  0.455

and,

Number of trials in which the event  F happens = 545

Probability of the event getting a tail, P(F) = 545/1000 = 0.545