Question

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

• A. True
• B. False

Answer 1

The correct option is A True

$\underset{–}{\text{Equally Likely Outcomes}:}$
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 $=\left\{\text{Red card, Black card}\right\}$

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

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

$\text{P(Red card)}=\frac{\text{Number of red cards}}{\text{Total number of cards}}$

$\text{P(Red card)}=\frac{26}{52}=\frac{26\times 1}{26\times 2}=\frac{1}{2}$ $(\because \text{In a standard deck of cards, total cards =52 and red cards = 26})$

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

$\text{P(Black card)}=\frac{26}{52}=\frac{26\times 1}{26\times 2}=\frac{1}{2}$ $(\because \text{In a standard deck of cards, total cards =52 and black cards = 26})$

Here, the probability of both the outcomes is equal. Hence, these are equally likely outcomes.

Therefore, the given statement is true.