Question

A standard deck of cards contains 52 cards.  One card is selected from the deck.

(a) Compute the probability of randomly selecting a club or spade.

(b)  Compute the probability of randomly selecting a club or spade or diamond.

(c)  Compute the probability randomly of randomly selecting a six or heart.

a.  P( club or spade)= (Type an interger or a simplified fraction)

b.  P(club or spade or diamond)=  (Type an interger or a simplified fraction)

c.  P(Six or heart)=  (Type an interger or a simplified fraction)

Answer 1

Concepts and reason

Probability is the state or an extent to which given event is likely to happen. In general, the probability is defined as a number between 0 and 1 where 0 implies the impossibility of an event to occur and 1 implies the certainty of an event to occur.

The probability calculation is used in this problem because random selection can be approximated by using probability.

Fundamentals

The formula needed to calculate the probabilities are as written below:

$p = \frac{{{\rm{Favourable outcomes}}}}{{{\rm{Total number of outcomes}}}}$

(a)

The calculation of the probability is as shown below:

$\begin{array}{c}\\p\left( {{\rm{Club or Spade}}} \right) = \frac{{13 + 13}}{{52}}\\\\ = \frac{{26}}{{52}}\\\\ = 0.5\\\end{array}$

(b)

The calculation of the probability is as shown below:

$\begin{array}{c}\\p\left( {{\rm{Club or Spade or Diamond}}} \right) = \frac{{13 + 13 + 13}}{{52}}\\\\ = \frac{{39}}{{52}}\\\\ = 0.75\\\end{array}$

(c)

The calculation of the probability is as shown below:

$\begin{array}{c}\\p\left( {{\rm{Six or heart}}} \right) = \frac{{3 + 13}}{{52}}\\\\ = \frac{{16}}{{52}}\\\\ = 0.30\\\end{array}$

Ans: Part a

The probability that for randomly selecting the club or spade is 0.5.