Question

Playing cards numbered from 1 to 20 are mixed thoroughly and kept it in a box. One card is taken at random from the box. What is the probability of the selected/drawn playing cards?1. Is a Prime number.2. A factor of 20.3. A composite number.4. A multiple of 3.5. A perfect square.

Answer 1

Explanation:

Probability is the ratio of the expected outcome (event) to the total outcome (sample space)

Probability = expected outcome/total outcome

If Playing cards numbered from 1 to 20 are mixed thoroughly and kept it in a box, the total number of sample space is 20

1) To calculate of getting a prima number.

Events = {2, 3, 5, 7,11,13,17,19}

n(events) = 8 elements

Pr(selecting a prime) = 8/20 = 2/5

2) If a factor of 20 is selected

Factor of 20 F = {2, 4, 5, 10, 20}

n(F) = 5

Pr(factor of 20) = 5/20 = 1/4

3) A composite number are 2 digits numbers.

Composite number C = {10,11,12,13,14,15,16,17,18,19,20}

n(C) = 11

Pr(a composite number) = 11/20

4) For multiple of 3.5

Multiple of 3.5 M = {3.5, 7.0, 10.5, 14.0, 17.5}

n(M) = 5

Pr(multiple of 3.5) = 5/20 = 1/4

5) For perfect squares

Perfect squares P = {1, 4, 9, 16}

n(P) = 4

Pr(perfect squares) = 4/20 = 1/5