Question

If a card is drawn from a standard deck of playing cards and sample space is defined as, sample space $=\left\{\text{Heart, Black}\right\}$, then the outcomes are equally likely.

• A. True
• B. False

Answer 1

The correct option is B False

$\underset{–}{\text{Equally Likely Outcomes}:}$
The outcomes in a sample space are $\text{equally likely}$ if each outcome has the $\text{same probability}$ of occurring.

A card is drawn and sample space is defined as, sample space $=\left\{\text{Heart, Black}\right\}$

In above given sample space, there are two outcomes 'Heart' and 'Black'.

And in a standard deck of cards,
Total number of cards $=52$
Number of heart cards $=13$
Number of black cards $=26$

Now, as we know, if a card is drawn from a deck of standard card,

$\text{P(Heart)}=\frac{\text{Number of heart cards}}{\text{Total number of cards}}$

$\text{P(Heart)}=\frac{13}{52}=\frac{13\times 1}{13\times 4}=\frac{1}{4}$

$\text{P(Black)}=\frac{\text{Number of black cards}}{\text{Total number of cards}}$

$\text{P(Black)}=\frac{26}{52}=\frac{26\times 1}{26\times 2}=\frac{1}{2}$

Here, the probabilities of the two outcomes are not equal, hence, these are not equally likely outcomes.

Therefore, the given statement is false.