Two coins are thrown at the same time, find the probability that different sides will fall on the coins.

In this case, there are 2 incompatible options, in which different sides will fall out on the coins:

A) 1O – 2P;

B) 1P – 2O;

Where 1, 2 – coins, O – heads, P – tails.

Their total probability can be calculated as the probability of the sum of inconsistent events P (C):

P (C) = P (A) + P (B).

The probability of variant A is calculated as the product of the probabilities of independent events (throwing of 2 coins):

P (A) = p1 * (1 – p2),

Where p1 is the probability of the first coin falling heads, (1 – p2) – the probability of the second coin falling tails.

Let’s calculate the probability of event B:

P (B) = (1 – p1) * p2,

Where (1 – p1) is the probability of the first coin hitting tails, p2 is the probability of the second coin falling heads.

Let’s determine the probability of the desired event:

P (C) = p1 * (1 – p2) + (1 – p1) * p2;

P (C) = 0.5 * (1 – 0.5) + (1 – 0.5) * 0.5 = 0.5.