There are four boxes $A_1,A_2,A_3 and A_4 box A_1$ hgas i cards and on each card a number is printed the number are from 1 to i. A box is selected randomly, the probability of selection of box $A_1 is \dfrac{i}{10}$ and then a card is drawn let $E_i$ represents the event that a card with number i is drawn. P(E_1) is equal to

Using the law of total probability, P(E_1) is the sum of the probabilities of drawing a card numbered 1 from each of the four boxes. The probability of selecting box A_i is i/10, and if box A_i is chosen, the chance of drawing the card numbered 1 is 1/i. Therefore, the total probability is the sum from i equals 1 to 4 of (i/10 times 1/i), which simplifies to 1/10 plus 1/10 plus 1/10 plus 1/10. This equals 4/10, resulting in a final probability of 1/5.

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