Thank you 1 A die is constructed so that a 1 or 2 occurs twi

Thank you!

1. A die is constructed so that a 1 or 2 occurs twice as often as a 5, and a 5 occurs three times as often as a 3, 4, or 6. If the die is tossed once, find the probability that (a) the number is even: (b) the number is a perfect square: (c) the number is greater than 4.

Solution

Let probability of 3,4,6 = x

Probability of 5 = 3x

so, probability of 1 or 2 = 6x

Nw, total probability has to be 1

So,

6x + 6x + x + x + 3x + x = 1

18x = 1

x = 1 / 18

a)

Probability of even number = P (2,4,6)

= 6x + x + x = 8x

= 8/18

= 4/9

b)

Probability of a perfect square = P (1,4)

= 6x + x

= 7x = 7/18

c)

Probability that number > 4

= P(5,6)

= 2x + x = 3x

= 3 / 18

= 1/6

Hope this helps., Ask if you have any doubts.