Question

A coin is tossed 500 times and we get heads 285 times and tails 215 times. When a coin is tossed at random, what is the probability of getting
(i) A head?
(ii)A tail?

Answer 1

Hint: The probability of any event is given by $\dfrac{{Number\,of\,times\,event\,occurs}}{{Total\,number\,of\,events}}$ .
In this question there are 2 events. The first event is of getting heads and second is of getting tails.
So, using the provided information, find the probabilities of getting head and tail individually by using the formula.
Complete step-by-step answer:
It is given that, a coin is tossed 500 times and we get heads 285 times.
Let H be the event that head appears on the coin. So, the probability of getting a head when a coin is tossed randomly is given by P(H).
$\therefore $ P(H) $ = \dfrac{{Number\,of\,times\,head\,appeared}}{{Total\,number\,of\,times\,coin\,tossed}}$
              $
   = \dfrac{{285}}{{500}} \\
   = \dfrac{{57}}{{100}} \\
 $
Thus, the probability of getting heads is 0.57.
Also, we get tails 215 times when we toss a coin 500 times.
Now, let T be the event that tail appears on the coin. So, the probability of getting a tail when a coin is tossed randomly is given by P(T).
$\therefore $ P(T) $ = \dfrac{{Number\,of\,times\,head\,appeared}}{{Total\,number\,of\,times\,coin\,tossed}}$
              $
   = \dfrac{{215}}{{500}} \\
   = \dfrac{{43}}{{100}} \\
 $
Thus, the probability of getting tails is 0.43.
So, P(H) = 0.57 and P(T) = 0.43.

Note: In general the probability of getting head is 0.5 and that of tail is 0.5.
But, here it is said that coins are tossed 500 times out of which we get heads 285 times and tail 215 times. So, the probabilities here will not be 0.5, but it will be calculated using $\dfrac{{Number\,of\,times\,event\,occurs}}{{Total\,number\,of\,events}}$ .
So, take a note that whenever there are certain number of events occurring and there are other events included in that, then we have to use the formula $\dfrac{{Number\,of\,times\,event\,occurs}}{{Total\,number\,of\,events}}$ .